Math question: 1+1=???

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Date: 06 Dec 2006 16:26:02
From: XaQ Morphy
Subject: Math question: 1+1=???

Please help me settle an argument with a friend. There's money and pride
involved. He's claiming there are certain mathematical instances where
1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
not a math genius, so I'm looking for help. Thanks!

Morphy
http://donkeymanifesto.blogspot.com

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Date: 06 Dec 2006 21:10:53
From: number6
Subject: Re: Math question: 1+1=???

Date: 07 Dec 2006 06:47:05
From: Tony Shek
Subject: Re: Math question: 1+1=???

You can do 1 (on the x axis) + 1 (on the y axis) = 0 (on the z axis)
Or in binary 1+1=10
It all depends on the numerical system.

--

Tony Shek
http://www.myspace.com/tonyshek
http://blog.myspace.com/tonyshek

"number6" <snumber6@aol.com > wrote in message
news:1165468253.095316.154870@f1g2000cwa.googlegroups.com...
>
> XaQ Morphy wrote:
>> Please help me settle an argument with a friend. There's money and pride
>> involved. He's claiming there are certain mathematical instances where
>> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
>> not a math genius, so I'm looking for help. Thanks!
>>
>>
>
> An mathematician's joke from my past was that 1+1=3 for sufficiently
> large values of 1 ...
>
> An engineer's joke was 1+1=3 to allow for expansion ...
>

Date: 06 Dec 2006 23:10:34
From: RazzO
Subject: Re: Math question: 1+1=???

Is this similar to The Peano Postulates?

On Dec 6 2006 10:47 PM, Tony Shek wrote:

> You can do 1 (on the x axis) + 1 (on the y axis) = 0 (on the z axis)
> Or in binary 1+1=10
> It all depends on the numerical system.
>
> --
>
>
> Tony Shek
> http://www.myspace.com/tonyshek
> http://blog.myspace.com/tonyshek
>
>
> "number6" <snumber6@aol.com> wrote in message
> news:1165468253.095316.154870@f1g2000cwa.googlegroups.com...
> >
> > XaQ Morphy wrote:
> >> Please help me settle an argument with a friend. There's money and pride
> >> involved. He's claiming there are certain mathematical instances where
> >> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> >> not a math genius, so I'm looking for help. Thanks!
> >>
> >>
> >
> > An mathematician's joke from my past was that 1+1=3 for sufficiently
> > large values of 1 ...
> >
> > An engineer's joke was 1+1=3 to allow for expansion ...
> >

RazzO
email:ticorazz (at) yahoo.com
http://www.razzo.com

--------
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Date: 07 Dec 10:39:28
From: Nick Wool
Subject: Re: Math question: 1+1=???

On Dec 7 2006 5:10 AM, number6 wrote:

> XaQ Morphy wrote:
> > Please help me settle an argument with a friend. There's money and pride
> > involved. He's claiming there are certain mathematical instances where
> > 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> > not a math genius, so I'm looking for help. Thanks!
> >
> >
>
> An mathematician's joke from my past was that 1+1=3 for sufficiently
> large values of 1 ...
>
> An engineer's joke was 1+1=3 to allow for expansion ...

And from an accountant's point of view; 1+1= whatever you want it to be.

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Date: 07 Dec 14:41:55
From: CHarrison100
Subject: Re: Math question: 1+1=???

On Dec 7 2006 5:39 AM, Nick Wool wrote:

>
>
>
> On Dec 7 2006 5:10 AM, number6 wrote:
>
> > XaQ Morphy wrote:
> > > Please help me settle an argument with a friend. There's money and pride
> > > involved. He's claiming there are certain mathematical instances where
> > > 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> > > not a math genius, so I'm looking for help. Thanks!
> > >
> > >
> >
> > An mathematician's joke from my past was that 1+1=3 for sufficiently
> > large values of 1 ...
> >
> > An engineer's joke was 1+1=3 to allow for expansion ...
>
> And from an accountant's point of view; 1+1= whatever you want it to be.
>

True. In the case of some public companies it is 1+1=What ever makes the stock
go up

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Date: 07 Dec 2006 15:04:30
From: Ayatollah Yootwiessalready
Subject: Re: Math question: 1+1=???

And then there's all those tricks you can do by using
matchsticks to make the 1+1 and then moving matches around

Date: 06 Dec 2006 20:22:08
From: FellKnight
Subject: Re: Math question: 1+1=???

On Dec 6 2006 5:26 PM, XaQ Morphy wrote:

> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!
>
> Morphy
> http://donkeymanifesto.blogspot.com

Don't make a bet with someone who seems to be claiming the impossible. He
is almost always right.

Fell
--
Website: www.fellknight.com
Email: fellknight at gmail dot com

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Date: 07 Dec 2006 07:26:59
From: Palooka
Subject: Re: Math question: 1+1=???

"FellKnight" <jordandevenport@hotmail.com > wrote in message
news:gghk44xsg3.ln2@recgroups.com...
> On Dec 6 2006 5:26 PM, XaQ Morphy wrote:
>
>> Please help me settle an argument with a friend. There's money and pride
>> involved. He's claiming there are certain mathematical instances where
>> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
>> not a math genius, so I'm looking for help. Thanks!
>>
>> Morphy
>> http://donkeymanifesto.blogspot.com
>
> Don't make a bet with someone who seems to be claiming the impossible. He
> is almost always right.
>
Sorry, can you repeat that? I can't hear you. Must be all this cider in my
ear.

Palooka

Date: 06 Dec 2006 19:43:27
From: Bill Ricardi
Subject: Re: Math question: 1+1=???

Date: 06 Dec 2006 18:59:44
From: ProEJockey
Subject: Re: Math question: 1+1=???

I don't think anyone covered this yet, but I am an engineer, and I have
heard this argument several times. The way I usually hear is is as such:

1+1=3, for large values of 1. what they are doing is rounding off 1.4 is
rounded to 1. so... 1.4 (1) plus 1.4 (1) equals 2.8 (3).

If I read it right, this is what they were getting at.

On Dec 6 2006 7:26 PM, XaQ Morphy wrote:

> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!
>
> Morphy
> http://donkeymanifesto.blogspot.com

ProEJockey

You can say any foolish thing to a dog, and the dog will give you a look
that says, My God, you're right! I never would've thought of that!

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Date: 06 Dec 2006 18:43:31
From:
Subject: Re: Math question: 1+1=???

XaQ Morphy wrote:
> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!
>
> Morphy
> http://donkeymanifesto.blogspot.com
>
> --------
> looking for a better newsgroup-reader? - www.recgroups.com

You friend is correct and it has to do with the overuse of the = sign
and the + sign. In many instances math people use the same symbol to
mean different things based on context. For example when you're doing
addition on say, integers like 1 + 1 = 2 you're actually doing a very
different thing then when you're adding two fractions like 2/3 + 1/3 =
1 and the same holds for real numbers like adding Pi to the square root
of 2. It's a subtle distinction but it can in fact help us understand
why you friend is right.

Rather then launching right into the math I'd rather give you a more
intuitive picture of what "sameness" means and how it relates to
equality. Lets say I give you a collection of objects, like a sweater,
an green apple, a goat and a gecko. Are any of these objects the same?
Well, if we are looking at them and saying "are they exactly alike in
every detail?" the answer is clearly no, but if we say "are they the
same color?" then for some of them like the gecko and the green apple
the answer is yes. We could also choose to divide our objects up in
animal or non-animal, and put them in the "same" container depending on
what category they fit into. In this case the gecko and the goat are
the "same" and the apple and the sweater are the "same". It's a simple
situation that shows clearly that CONTEXT plays a large part in what we
consider equality.

So what contexts are valid? As it turns out, if we're given any
collection of objects we can partition that collection and simply say
anything in the same section is "equal" to the other. Notice how this
parallels the situation where we split the animals from the
non-animals. Sometimes these partitions have a greater meaning and
sometimes they're just random, however all such partitions properly
define what's known as an "equivalence relation" on the set of objects.

So what does this have to do with our old fashioned equal sign? Well,
firstly when we think of the equals sign we're not really thinking
about sorting a collection of objects, we're thinking about certain
universal rules about how we can manipulate equations. Those rules have
been well worked out by mathematicians and I'll give them to you now.

1) Something is always the same as itself ( A = A )

2) If some object is the same as another, then that object is the same
as the original. ( if A = B then B = A)

3) If some object is the same as another, and that other object is the
same as a third, then the first is the same as the third. ( If A = B
and B = C then A = C).

Now these seem rather obvious to us when we use the equals sign, but
note that if we replaced it with say, a > sign that number 2) would be
false. You need all three of these to capture the idea of equality. I
will leave it to you to verify that the idea of partitioning a
collection of objects will have any two objects in the same bin
satisfying these three rules.

So now for the math and an example of when 1 + 1 = 0. I'm going to
DEFINE a new equivalence relation on the natural numbers. We're going
to say that any two numbers x and y are the same if and only if x - y
is a multiple of 2 including negative multiples. So for example 5 and 3
are the same because 5 - 3 = 2 and 6 and 2 are the same because 6 - 2 =
4 which is a multiple of 2. However 6 and 3 are NOT the same because 6
- 3 = 3 which is not a multiple of 2. I will again leave it to you to
verify that all the even numbers are equal to each other and all the
odd numbers are equal to other odds numbers. Since by rule 3) and the
fact that 2 - 0 = 2 we know that 0 is in the same group with the even
numbers and that means that 2 equals 0. This is commonly known as
arithmetic modulo 2 and in this sort of system, 1+1 = 0.

I hope that makes some sense of the issue for you.

Cheers, Abe

Date: 06 Dec 2006 18:42:46
From:
Subject: Re: Math question: 1+1=???

XaQ Morphy wrote:
> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!
>
> Morphy
> http://donkeymanifesto.blogspot.com
>
> --------
> looking for a better newsgroup-reader? - www.recgroups.com

You friend is correct and it has to do with the overuse of the = sign
and the + sign. In many instances math people use the same symbol to
mean different things based on context. For example when you're doing
addition on say, integers like 1 + 1 = 2 you're actually doing a very
different thing then when you're adding two fractions like 2/3 + 1/3 =
1 and the same holds for real numbers like adding Pi to the square root
of 2. It's a subtle distinction but it can in fact help us understand
why you friend is right.

Rather then launching right into the math I'd rather give you a more
intuitive picture of what "sameness" means and how it relates to
equality. Lets say I give you a collection of objects, like a sweater,
an green apple, a goat and a gecko. Are any of these objects the same?
Well, if we are looking at them and saying "are they exactly alike in
every detail?" the answer is clearly no, but if we say "are they the
same color?" then for some of them like the gecko and the green apple
the answer is yes. We could also choose to divide our objects up in
animal or non-animal, and put them in the "same" container depending on
what catagory they fit into. In this case the gecko and the goat are
the "same" and the apple and the sweater are the "same". It's a simple
situation that shows clearly that CONTEXT plays a large part in what we
consider equality.

So what contexts are valid? As it turns out, if we're given any
collection of objects we can partition that collection and simply say
anything in the same section is "equal" to the other. Notice how this
parallels the situation where we split the animals from the
non-animals. Sometimes these partitions have a greater meaning and
sometimes they're just random, however all such partitions properly
define what's known as an "equivilence relation" on the set of objects.

So what does this have to do with our old fashioned equal sign? Well,
firstly when we think of the equals sign we're not really thinking
about sorting a collection of objects, we're thinking about certain
universal rules about how we can manipulate equations. Those rules have
been well worked out by mathamaticans and I'll give them to you now.

1) Something is always the same as itself ( A = A )

2) If some object is the same as another, then that object is the same
as the original. ( if A = B then B = A)

3) If some object is the same as another, and that other object is the
same as a third, then the first is the same as the third. ( If A = B
and B = C then A = C).

Now these seem rather obvious to us when we use the equals sign, but
note that if we replaced it with say, a > sign that number 2) would be
false. You need all three of these to capture the idea of equality. I
will leave it to you to verify that the idea of partitioning a
collection of objects will have any two objects in the same bin
satisfying these three rules.

So now for the math and an example of when 1 + 1 = 0. I'm going to
DEFINE a new equivalence relation on the natural numbers. We're going
to say that any two numbers x and y are the same if and only if x - y
is a multiple of 2 including negative multiples. So for example 5 and 3
are the same because 5 - 3 = 2 and 6 and 2 are the same because 6 - 2 =
4 which is a multiple of 2. However 6 and 3 are NOT the same because 6
- 3 = 3 which is not a multiple of 2. I wil again leave it to you to
verify that all the even numbers are equal to each other and all the
odd numbers are equal to other odds numbers. Since by rule 3) and the
fact that 2 - 0 = 2 we know that 0 is in the same group with the even
numbers and that means that 2 equals 0. This is commonly known as
arithmatic modulo 2 and in this sort of system, 1+1 = 0.

I hope that makes some sense of the issue for you.

Cheers, Abe

Date: 06 Dec 2006 19:08:10
From:
Subject: Re: Math question: 1+1=???

Gary Carson wrote:
> On Dec 6 2006 8:42 PM, abe.buckingham@gmail.com wrote:
>
> >
> > 3) If some object is the same as another, and that other object is the
> > same as a third, then the first is the same as the third. ( If A = B
> > and B = C then A = C).
>
> That depends on what you mean by object.
>
>
> Gary Carson
> http://www.garycarson.com
>
>
>
> _______________________________________________________________
> Your Online Poker Community - http://www.recpoker.com

Then to dispell an ambiguity I mean an element of a well defined set in
ZFC.

Date: 06 Dec 2006 19:44:59
From:
Subject: Re: Math question: 1+1=???

Gary Carson wrote:
> On Dec 6 2006 9:08 PM, abe.buckingham@gmail.com wrote:
>
> > >
> > > That depends on what you mean by object.
> > >
> > >
> > > Gary Carson
> > > http://www.garycarson.com/
> > >
> > >
> > >
> > > _______________________________________________________________
> > > Your Online Poker Community - /
> >
> > Then to dispell an ambiguity I mean an element of a well defined set in
> > ZFC.
>
> I had no idea that a set that wasn't well defined was a set and I have no idea
> what ZFC is.
>
> But I still think you're probably wrong.
>
> When you intentially mouth of in a way that you hope won't be clear while
> claiming that you're trying to clarify then it's almost always a good bet that
> you're full of shit.
>
>
> Gary Carson
> http://www.garycarson.com
>
>
>
> _______________________________________________________________
> Watch Lists, Block Lists, Favorites - http://www.recpoker.com

Sorry thought you were asking more precise math question. ZFC is a
common acronym and you can read more about it at the link provided
below. If you had some paticular object in mind that you feel refutes
my examples I'd love to see them.

http://en.wikipedia.org/wiki/Zermelo%E2%80%93Fraenkel_set_theory

Date: 07 Dec
From: Gary Carson
Subject: Re: Math question: 1+1=???

On Dec 6 2006 9:08 PM, abe.buckingham@gmail.com wrote:

> >
> > That depends on what you mean by object.
> >
> >
> > Gary Carson
> > http://www.garycarson.com/
> >
> >
> >
> > _______________________________________________________________
> > Your Online Poker Community - /
>
> Then to dispell an ambiguity I mean an element of a well defined set in
> ZFC.

I had no idea that a set that wasn't well defined was a set and I have no idea
what ZFC is.

But I still think you're probably wrong.

When you intentially mouth of in a way that you hope won't be clear while
claiming that you're trying to clarify then it's almost always a good bet that
you're full of shit.

Gary Carson
http://www.garycarson.com

_______________________________________________________________
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Date: 07 Dec 10:37:09
From: Nick Wool
Subject: Re: Math question: 1+1=???

On Dec 7 2006 3:26 AM, Gary Carson wrote:

>
> When you intentially mouth of in a way that you hope won't be clear while
> claiming that you're trying to clarify then it's almost always a good bet that
> you're full of shit.

> Gary Carson
> http://www.garycarson.com

Thanks, dear mr carson...this one is a classic...May I borrow this sentence from
you?

It could be useful for replying to your...er...more interesting points in the
future.

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Date: 07 Dec
From: Gary Carson
Subject: Re: Math question: 1+1=???

On Dec 6 2006 8:42 PM, abe.buckingham@gmail.com wrote:

>
> 3) If some object is the same as another, and that other object is the
> same as a third, then the first is the same as the third. ( If A = B
> and B = C then A = C).

That depends on what you mean by object.

Gary Carson
http://www.garycarson.com

_______________________________________________________________
Your Online Poker Community - http://www.recpoker.com

Date: 06 Dec 2006 19:31:08
From: cquinn
Subject: Re: Math question: 1+1=???

Synergy is where the result of combining 1+1 is greater than the sum of the
parts. Its a common term in business takeovers. Also, any marriage resulting
in children is another example.

Qdog223

"XaQ Morphy" <a1c5905@webnntp.invalid > wrote in message
news:ql3k44xps2.ln2@recgroups.com...
> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!
>
> Morphy
> http://donkeymanifesto.blogspot.com
>
> --------
> looking for a better newsgroup-reader? - www.recgroups.com
>
>

Date: 07 Dec
From: Gary Carson
Subject: Re: Math question: 1+1=???

Never take another guys prop bet. You'll get cider in your ear.

Without thinking hard I can think of two.

One is if you allow division by zero. You can prove that 1+1=1 by allowing
division by zero. In fact you can prove any nonsense you want by allowing
division by zero, which is why we don't allow it. Zero is special.

Also if you allow him to confuse math with the notation used to communicate math
then 1+1 = 10 in base 2.

I'm sure there are others. They are all meaningless (except for division by
zero, that's an important one).
On Dec 6 2006 6:26 PM, XaQ Morphy wrote:

> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!
>
> Morphy
> http://donkeymanifesto.blogspot.com/
Gary Carson
http://www.garycarson.com

_______________________________________________________________
Posted using RecPoker.com v2.2 - http://www.recpoker.com

Date: 06 Dec 2006 16:54:46
From:
Subject: Re: Math question: 1+1=???

> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!

If you look at abstract algebra, your friend is correct. Our number
system is arbitrary. We have assigned names to various number and
created rules for how they work.

But mathematicians can and do create other number systems. You could
create a system where 1+1 = 0 (which is how a 1-bit computer would work
for instance).

But in the world we normally inhabit - using the integers we all know
and love as our algebraic system, 1 + 1 = 2.

Date: 06 Dec 2006 16:54:23
From: Old Wolf
Subject: Re: Math question: 1+1=???

Date: 07 Dec 2006 09:22:41
From: Ayatollah Yootwiessalready
Subject: Re: Math question: 1+1=???

In article <1165452863.489672.218370
@n67g2000cwd.googlegroups.com >, oldwolf@inspire.net.nz says...
> XaQ Morphy wrote:
> > Please help me settle an argument with a friend. There's money and pride
> > involved. He's claiming there are certain mathematical instances where
> > 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> > not a math genius, so I'm looking for help. Thanks!
>
> It's all philosophy really. People who claim 1 + 1 is something
> else, are trying to make statements about the nature of addition
> and numbers and what-not (or they're being silly).
>
> Is your friend able to actually come up with one of these
> certain instances ?
>
> Perhaps he is thinking of situations like base 2, where 1 + 1 = 10
> (but that is just another way of writing 2).
>
> Another possibility might be if he is thinking of group theory,
> eg. in the group called "C2", 1+1 = 0. But in this case, '+' has
> been re-defined to something different to what it means to most
> people. Moreover, 0 = 2 in this situation. So it comes back to
> arguing about what you mean by '+' and '1' and '2'.
>
>
also in boolean algebra, "1+1" means "true or true", which is
true, which is 1

Date: 07 Dec 17:57:55
From: CHarrison100
Subject: Re: Math question: 1+1=???

On Dec 6 2006 7:26 PM, XaQ Morphy wrote:

> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!
>
> Morphy
> http://donkeymanifesto.blogspot.com/

What about (-1) + (+1) = 0

_______________________________________________________________
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Date: 07 Dec 2006 06:27:55
From: Eddie
Subject: Re: Math question: 1+1=???

How bored were you when you had this arguement?

XaQ Morphy wrote:
> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!
>
> Morphy
> http://donkeymanifesto.blogspot.com
>
> --------
> looking for a better newsgroup-reader? - www.recgroups.com

Date: 07 Dec 2006 08:29:30
From: FellKnight
Subject: Re: Math question: 1+1=???

On Dec 7 2006 7:27 AM, Eddie wrote:

> How bored were you when you had this arguement?

What argument?

Fell
--
Website: www.fellknight.com
Email: fellknight at gmail dot com

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Date:
From:
Subject:

Date: 07 Dec 2006 00:26:49
From: Erik Max Francis
Subject: Re: Math question: 1+1=???

Date: 07 Dec 2006 04:45:44
From:
Subject: Re: Math question: 1+1=???

Gary Carson wrote:
> On Dec 7 2006 2:27 AM, Erik Max Francis wrote:
>
> > XaQ Morphy wrote:
> >
> > > Please help me settle an argument with a friend. There's money and pride
> > > involved. He's claiming there are certain mathematical instances where
> > > 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> > > not a math genius, so I'm looking for help. Thanks!
> >
> > "Certain mathematical instances" is probably enough cover for him to win
> > the bet. In all circumstances where 1 and 2 are integers, + is an
> > operation over integers, and = is an equality operation over integers,
> > then 1 + 1 = 2 is always true, without exceptions.
>
> How about if we define 0/0 as 1?
>
> >
>
> Gary Carson
> http://www.garycarson.com
>
>
>
> _______________________________________________________________
> Block Lists, Favorites, and more - http://www.recpoker.com

You can of course define 0/0 to be 1, but it's not very interesting or
useful since common operations like addition and multiplication no
longer have a useful meaning under such a scheme and it doesn't help
the 1 + 1 = ? line of reasoning.

Date: 07 Dec 2006 14:35:48
From: Tom White
Subject: Re: Math question: 1+1=???

abe.buckingham@gmail.com wrote:
+ You can of course define 0/0 to be 1, but it's not very interesting or
+ useful since common operations like addition and multiplication no
+ longer have a useful meaning under such a scheme and it doesn't help
+ the 1 + 1 = ? line of reasoning.

x = y

x^2 = xy

x^2 - y^2 = xy - y^2

(x+y)(x-y) = y(x-y)

x+y = y

I recommend not allowing division by zero, but I would
call it interesting - particularly in the field of Bar
Betting.

Date: 08 Dec 2006 16:42:20
From: Erik Max Francis
Subject: Re: Math question: 1+1=???

Tom White wrote:

> I recommend not allowing division by zero, but I would
> call it interesting - particularly in the field of Bar
> Betting.

This isn't a proof of anything, because the proof is invalid. Dividing
by zero is the same as making any other illegal step in a proof;
whatever results you come up with are invalid. A logically invalid
proof is meaningless.

--
Erik Max Francis && max@alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM, Y!M erikmaxfrancis
One cannot always be a hero, but one can always be a man.
-- Goethe

Date: 07 Dec 2006 05:06:07
From:
Subject: Re: Math question: 1+1=???

Gary Carson wrote:
> On Dec 7 2006 6:45 AM, abe.buckingham@gmail.com wrote:
>
> > Gary Carson wrote:
> > > On Dec 7 2006 2:27 AM, Erik Max Francis wrote:
> > >
> > > > XaQ Morphy wrote:
> > > >
> > > > > Please help me settle an argument with a friend. There's money and pride
> > > > > involved. He's claiming there are certain mathematical instances where
> > > > > 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> > > > > not a math genius, so I'm looking for help. Thanks!
> > > >
> > > > "Certain mathematical instances" is probably enough cover for him to win
> > > > the bet. In all circumstances where 1 and 2 are integers, + is an
> > > > operation over integers, and = is an equality operation over integers,
> > > > then 1 + 1 = 2 is always true, without exceptions.
> > >
> > > How about if we define 0/0 as 1?
> > >
> > > >
> > >
> > > Gary Carson
> > > http://www.garycarson.com/
> > >
> > >
> > >
> > > _______________________________________________________________
> > > Block Lists, Favorites, and more - /
> >
> > You can of course define 0/0 to be 1, but it's not very interesting or
> > useful since common operations like addition and multiplication no
> > longer have a useful meaning under such a scheme and it doesn't help
> > the 1 + 1 = ? line of reasoning.
>
> What line of reasoning? If you allow division by zero you can prove 1+1 = any
> damn thing you want with normal defintions for the + operation, for the =
> relation and for the integers 1 and 2.
>
> All you're saying is that it doesn't help to demonstrate a situation where your
> assertion is wrong. Okay. It doesn't. But why should anybody give a shit
> about that?
>
>
> Gary Carson
> http://www.garycarson.com
>
>
>
> _______________________________________________________________
> Block Lists, Favorites, and more - http://www.recpoker.com

If you define 0/0 to be 1 then + no longer has the same meaning and
needs to be redefined as well since we've betrayed the axioms of a
field.

http://en.wikipedia.org/wiki/Field_%28mathematics%29

As an aside you might be interested to know that some objects in
abstract algebra do allow zero divisors in a meaningful context. You
can read more about Rings and zero divisors here.

http://en.wikipedia.org/wiki/Ring_%28mathematics%29
http://en.wikipedia.org/wiki/Zero_divisor

Date: 07 Dec 12:56:20
From: Gary Carson
Subject: Re: Math question: 1+1=???

On Dec 7 2006 6:45 AM, abe.buckingham@gmail.com wrote:

> Gary Carson wrote:
> > On Dec 7 2006 2:27 AM, Erik Max Francis wrote:
> >
> > > XaQ Morphy wrote:
> > >
> > > > Please help me settle an argument with a friend. There's money and pride
> > > > involved. He's claiming there are certain mathematical instances where
> > > > 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> > > > not a math genius, so I'm looking for help. Thanks!
> > >
> > > "Certain mathematical instances" is probably enough cover for him to win
> > > the bet. In all circumstances where 1 and 2 are integers, + is an
> > > operation over integers, and = is an equality operation over integers,
> > > then 1 + 1 = 2 is always true, without exceptions.
> >
> > How about if we define 0/0 as 1?
> >
> > >
> >
> > Gary Carson
> > http://www.garycarson.com/
> >
> >
> >
> > _______________________________________________________________
> > Block Lists, Favorites, and more - /
>
> You can of course define 0/0 to be 1, but it's not very interesting or
> useful since common operations like addition and multiplication no
> longer have a useful meaning under such a scheme and it doesn't help
> the 1 + 1 = ? line of reasoning.

What line of reasoning? If you allow division by zero you can prove 1+1 = any
damn thing you want with normal defintions for the + operation, for the =
relation and for the integers 1 and 2.

All you're saying is that it doesn't help to demonstrate a situation where your
assertion is wrong. Okay. It doesn't. But why should anybody give a shit
about that?

Gary Carson
http://www.garycarson.com

_______________________________________________________________
Block Lists, Favorites, and more - http://www.recpoker.com

Date: 07 Dec 12:00:17
From: Gary Carson
Subject: Re: Math question: 1+1=???

On Dec 7 2006 2:27 AM, Erik Max Francis wrote:

> XaQ Morphy wrote:
>
> > Please help me settle an argument with a friend. There's money and pride
> > involved. He's claiming there are certain mathematical instances where
> > 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> > not a math genius, so I'm looking for help. Thanks!
>
> "Certain mathematical instances" is probably enough cover for him to win
> the bet. In all circumstances where 1 and 2 are integers, + is an
> operation over integers, and = is an equality operation over integers,
> then 1 + 1 = 2 is always true, without exceptions.

How about if we define 0/0 as 1?

>

Gary Carson
http://www.garycarson.com

_______________________________________________________________
Block Lists, Favorites, and more - http://www.recpoker.com

Date: 07 Dec 14:52:29
From: CHarrison100
Subject: Re: Math question: 1+1=???

On Dec 7 2006 7:00 AM, Gary Carson wrote:

>
>
>
> On Dec 7 2006 2:27 AM, Erik Max Francis wrote:
>
> > XaQ Morphy wrote:
> >
> > > Please help me settle an argument with a friend. There's money and pride
> > > involved. He's claiming there are certain mathematical instances where
> > > 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> > > not a math genius, so I'm looking for help. Thanks!
> >
> > "Certain mathematical instances" is probably enough cover for him to win
> > the bet. In all circumstances where 1 and 2 are integers, + is an
> > operation over integers, and = is an equality operation over integers,
> > then 1 + 1 = 2 is always true, without exceptions.
>
> How about if we define 0/0 as 1?
>
> >
>
> Gary Carson
> http://www.garycarson.com
>
>

so if 0/0 = 1 then 1+1= can be writen 0/0 + 0/0 = so the answer is 0/0 or 1

This is if you ignore the divide by 0 rule

_______________________________________________________________
The Largest Online Poker Community - http://www.recpoker.com

Date: 08 Dec 2006 16:40:49
From: Erik Max Francis
Subject: Re: Math question: 1+1=???

Gary Carson wrote:

> On Dec 7 2006 2:27 AM, Erik Max Francis wrote:
>
>> XaQ Morphy wrote:
>>
>>> Please help me settle an argument with a friend. There's money and pride
>>> involved. He's claiming there are certain mathematical instances where
>>> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
>>> not a math genius, so I'm looking for help. Thanks!
>
>> "Certain mathematical instances" is probably enough cover for him to win
>> the bet. In all circumstances where 1 and 2 are integers, + is an
>> operation over integers, and = is an equality operation over integers,
>> then 1 + 1 = 2 is always true, without exceptions.
>
> How about if we define 0/0 as 1?

Then you're not talking about the integers we all know and love.
Division by zero is undefined on the integers, so 0/0 is undefined.

--
Erik Max Francis && max@alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM, Y!M erikmaxfrancis
One cannot always be a hero, but one can always be a man.
-- Goethe

Date: 07 Dec 2006 18:21:21
From: Old Wolf
Subject: Re: Math question: 1+1=???

Jim Mercurio wrote:
> Now, let's talk about infinity.

Did you know that a schoolteacher has now taught his students
how to divide by 0, and thus solve problems that Newton and
Pythagoras could not solve?

http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml

Date: 07 Dec 2006 16:30:07
From: kurtissimo
Subject: Re: Math question: 1+1=???

On Dec 6 2006 8:26 PM, XaQ Morphy wrote:

> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!

Will you settle for a proof that 0 = 1? :)

Start with 0. If you add zero infinitely many times, what do you get?
You still get zero, of course! So, 0 = 0 + 0 + 0 + 0 + .......
But 0 = 1 - 1. So, we substitute 1 - 1 for 0, to get.......

0 = (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + .......

Keeping in mind, again, that this is an *infinite* sum - meaning we never
run out of 1's or -1's - we can rewrite the above equation as follows:

0 = 0 + 0 + 0 + 0 + 0 + 0 + ......
0 = (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + .......
0 = 1 - 1 + 1 - 1 + 1 - 1 + 1 - 1 + ......
0 = 1 + (-1) + 1 + (-1) + 1 + (-1) + 1 + (-1) + 1 + ......
0 = 1 + (-1 + 1) + (-1 + 1) + (-1 + 1) + (-1 + 1) + ......
0 = 1 + 0 + 0 + 0 + 0 + .....
0 = 1. QED

(Corollary: You owe me a dollar.)

------
RecGroups : the community-oriented newsreader : www.recgroups.com

Date: 07 Dec 2006 16:13:49
From: Jim Mercurio
Subject: Re: Math question: 1+1=???

There is a more simple way to look at this. 1 + 1 = 1 if the first two
ones happen to be the same thing.

How many world class players in their 20s are named Phil.

How many world class players have the last name Ivey.

the answer to each question is one, so if you had a party and invited
each person who satifies these sentences, you would end up with one
person there.

Now, let's talk about infinity.

Did you know there are the same amount of positive integers as there
are all integers (positive and negative) and that there are more
numbers between 0 and 1 than there are all integers.

The proofs are easy too.

Jim

XaQ Morphy wrote:
> > The troll-o-meter would have rated this very highly indeed, but somewhere in
> > the thread you responded to something. This surely breaches the best
> > traditions, n'est ce pas?
>
> Why, whatever do you mean?
>
> [18:21] thenutlow: its always the most basic simplistic fucking threads in
> the world that get the most replies
> [18:23] thenutlow: the thread "OT: What is one plus one?"
> [18:23] thenutlow: would get 400 replies
> [18:23] XaQ Morphy: lol
> [18:24] XaQ Morphy: that gives me an idea
>
>
> Morphy
> http://donkeymanifesto.blogspot.com
>
> ---
> : the next generation of web-newsreaders : http://www.recgroups.com

Date: 07 Dec 2006 19:57:31
From:
Subject: Re: Math question: 1+1=???

Gary Carson wrote:
> On Dec 7 2006 6:13 PM, Jim Mercurio wrote:
>
> > There is a more simple way to look at this. 1 + 1 = 1 if the first two
> > ones happen to be the same thing.
> >
> > How many world class players in their 20s are named Phil.
> >
> > How many world class players have the last name Ivey.
> >
> > the answer to each question is one, so if you had a party and invited
> > each person who satifies these sentences, you would end up with one
> > person there.
> >
> > Now, let's talk about infinity.
> >
> > Did you know there are the same amount of positive integers as there
> > are all integers (positive and negative) and that there are more
> > numbers between 0 and 1 than there are all integers.
> >
> > The proofs are easy too.
>
> Do those proofs involve counting things that aren't countable?
>
> Gary Carson
> http://www.garycarson.com
>
>
>
> _______________________________________________________________
> The Largest Online Poker Community - http://www.recpoker.com

That's either a really clever pun or an amazing coincidence.

Date: 07 Dec 2006 18:59:34
From: Jim Mercurio
Subject: Re: Math question: 1+1=???

Gary Carson wrote:
> On Dec 7 2006 6:13 PM, Jim Mercurio wrote:
>
> > There is a more simple way to look at this. 1 + 1 = 1 if the first two
> > ones happen to be the same thing.
> >
> > How many world class players in their 20s are named Phil.
> >
> > How many world class players have the last name Ivey.
> >
> > the answer to each question is one, so if you had a party and invited
> > each person who satifies these sentences, you would end up with one
> > person there.
> >
> > Now, let's talk about infinity.
> >
> > Did you know there are the same amount of positive integers as there
> > are all integers (positive and negative) and that there are more
> > numbers between 0 and 1 than there are all integers.
> >
> > The proofs are easy too.
>
> Do those proofs involve counting things that aren't countable?
>
> Gary Carson

There are ways of counting them. They call the infinity that has "the
same number of elements" as integers aleph null. And yes, by
mathematician's definition of an "uncountable set", the set of all
numbers between 0 and 1 are uncountable. (but they are countable, I
think) There are "more" numbers between 0 and 1 then there are all
integers. But the set of positive integers, the set of even integers,
the set of odd integers and the set of all integers ironically are the
exact same size. In fact, if I remember, an infinite set is a set
which can be put into a one to one correspondence with a proper subset
(a subset that has less than the original) of itself.

Date: 07 Dec 2006 20:21:02
From: kurtissimo
Subject: Re: Math question: 1+1=???

On Dec 7 2006 10:59 PM, Jim Mercurio wrote:
> Gary Carson wrote:
> > On Dec 7 2006 6:13 PM, Jim Mercurio wrote:
> > Do those proofs involve counting things that aren't countable?
> > Gary Carson
>
> There are ways of counting them. They call the infinity that has "the
> same number of elements" as integers aleph null.

The math-nerd term is "cardinality" - as in, the set of integers, the set
of natural numbers, and the set of rational numbers all have the same
cardinality, which is aleph-zero (or "aleph-null" if you're a damn
foreigner (just kidding)). A set has cardinality aleph-zero, or
(equivalently) is "countable", if there's a way to define a *list* which,
if carried out far enough, will include any given element of the set.

That's what "countable" *usually* means, at least. Which is why I'm about
to be confused.....

> And yes, by
> mathematician's definition of an "uncountable set", the set of all
> numbers between 0 and 1 are uncountable. (but they are countable, I
> think).

I was with you up to here. But by what definition of "countable" are the
real numbers between 0 and 1 countable? The Cantor diagonalization
argument demonstrates that any attempt to list the elements of this set is
doomed to fail. So do you have a different definition of "countable" in
mind? Just wondering.

_____________________________________________________________________
: the next generation of web-newsreaders : http://www.recgroups.com

Date: 08 Dec
From: Gary Carson
Subject: Re: Math question: 1+1=???

On Dec 7 2006 6:13 PM, Jim Mercurio wrote:

> There is a more simple way to look at this. 1 + 1 = 1 if the first two
> ones happen to be the same thing.
>
> How many world class players in their 20s are named Phil.
>
> How many world class players have the last name Ivey.
>
> the answer to each question is one, so if you had a party and invited
> each person who satifies these sentences, you would end up with one
> person there.
>
> Now, let's talk about infinity.
>
> Did you know there are the same amount of positive integers as there
> are all integers (positive and negative) and that there are more
> numbers between 0 and 1 than there are all integers.
>
> The proofs are easy too.

Do those proofs involve counting things that aren't countable?

Gary Carson
http://www.garycarson.com

_______________________________________________________________
The Largest Online Poker Community - http://www.recpoker.com

Date: 08 Dec 2006 06:44:06
From: number6
Subject: Re: Math question: 1+1=???

kurtissimo wrote:
> > There are ways of counting them. They call the infinity that has "the
> > same number of elements" as integers aleph null.

Issac Asimov quite a while back wrote a math essay .. where he compared
some backward native population counting the numbers "1,2, many" with
no additional words for numbers over 2 ... then went to illustrate our
counting of infinities aleph(0),aleph(1),aleph(2) ...and how they
related ... but we have no concept of aleph(3) ... so in counting
infinities we were as backward as those natives ...

Date: 08 Dec 2006 06:02:52
From: Jim Mercurio
Subject: Re: Math question: 1+1=???

I was playing with semantics. If the cardinality of that uncountable
set is c, then we have just found a way to "count" it.

Back to pot odds, implied odds, effective odds and Steve Dannenman's
home game for me.

Jim

abe.buckingham@gmail.com wrote:
> Jim Mercurio wrote:
> > >
> > > I was with you up to here. But by what definition of "countable" are the
> > > real numbers between 0 and 1 countable? The Cantor diagonalization
> > > argument demonstrates that any attempt to list the elements of this set is
> > > doomed to fail. So do you have a different definition of "countable" in
> > > mind? Just wondering.
> > >
> > >
> >
> > I was playing with semantics. "uncountable" doesn't mean not
> > countable. They have name they give to the "infinity" of "how many
> > real numbers between 0 and 1, right? Isn't that C. So they do count
> > the set, but it happens to be an uncountable set by the definition that
> > it can't be put into a 1-1 mapping of the integers.
> >
> > This whole topic is a cluster-point fuck. ;-)
> > Topologically yours,
> > Jim
>
> Just so we're clear uncountable sets are NOT countable. I can "count"
> an infinite set in the sense that I can keep going and going - there is
> always an action that will eventually get me to any member of the set.
> However for uncountable sets no such action exists, and it's this
> action that we call "counting".
>
> As for the numbers between 0 and 1 being called c that is true, and
> the question of "does c = alph_1?" depends on your acceptance or
> rejection of the continuum hypothesis.
>
> Are you familar with Cantor's first arguement for the uncountability of
> the reals? It avoids some of the sticky points of diagonlization that
> so many cranks get caught up on. You can check it out here.
>
> http://en.wikipedia.org/wiki/Cantor%27s_first_uncountability_proof

Date: 08 Dec 2006 05:06:51
From:
Subject: Re: Math question: 1+1=???

Jim Mercurio wrote:
> >
> > I was with you up to here. But by what definition of "countable" are the
> > real numbers between 0 and 1 countable? The Cantor diagonalization
> > argument demonstrates that any attempt to list the elements of this set is
> > doomed to fail. So do you have a different definition of "countable" in
> > mind? Just wondering.
> >
> >
>
> I was playing with semantics. "uncountable" doesn't mean not
> countable. They have name they give to the "infinity" of "how many
> real numbers between 0 and 1, right? Isn't that C. So they do count
> the set, but it happens to be an uncountable set by the definition that
> it can't be put into a 1-1 mapping of the integers.
>
> This whole topic is a cluster-point fuck. ;-)
> Topologically yours,
> Jim

Just so we're clear uncountable sets are NOT countable. I can "count"
an infinite set in the sense that I can keep going and going - there is
always an action that will eventually get me to any member of the set.
However for uncountable sets no such action exists, and it's this
action that we call "counting".

As for the numbers between 0 and 1 being called c that is true, and
the question of "does c = alph_1?" depends on your acceptance or
rejection of the continuum hypothesis.

Are you familar with Cantor's first arguement for the uncountability of
the reals? It avoids some of the sticky points of diagonlization that
so many cranks get caught up on. You can check it out here.

http://en.wikipedia.org/wiki/Cantor%27s_first_uncountability_proof

Date: 08 Dec 2006 04:52:12
From: Jim Mercurio
Subject: Re: Math question: 1+1=???

>
> I was with you up to here. But by what definition of "countable" are the
> real numbers between 0 and 1 countable? The Cantor diagonalization
> argument demonstrates that any attempt to list the elements of this set is
> doomed to fail. So do you have a different definition of "countable" in
> mind? Just wondering.
>
>

I was playing with semantics. "uncountable" doesn't mean not
countable. They have name they give to the "infinity" of "how many
real numbers between 0 and 1, right? Isn't that C. So they do count
the set, but it happens to be an uncountable set by the definition that
it can't be put into a 1-1 mapping of the integers.

This whole topic is a cluster-point fuck. ;-)
Topologically yours,
Jim

Date: 11 Dec 2006 10:41:38
From: Grip
Subject: Re: Math question: 1+1=???

Hey are you the screenplay Jim Mercurio? I was at a workshop of yours
in Abq a couple of years back. Good stuff man.

G

Jim Mercurio wrote:
> I was playing with semantics. If the cardinality of that uncountable
> set is c, then we have just found a way to "count" it.
>
> Back to pot odds, implied odds, effective odds and Steve Dannenman's
> home game for me.
>
> Jim
>
>
> abe.buckingham@gmail.com wrote:
> > Jim Mercurio wrote:
> > > >
> > > > I was with you up to here. But by what definition of "countable" are the
> > > > real numbers between 0 and 1 countable? The Cantor diagonalization
> > > > argument demonstrates that any attempt to list the elements of this set is
> > > > doomed to fail. So do you have a different definition of "countable" in
> > > > mind? Just wondering.
> > > >
> > > >
> > >
> > > I was playing with semantics. "uncountable" doesn't mean not
> > > countable. They have name they give to the "infinity" of "how many
> > > real numbers between 0 and 1, right? Isn't that C. So they do count
> > > the set, but it happens to be an uncountable set by the definition that
> > > it can't be put into a 1-1 mapping of the integers.
> > >
> > > This whole topic is a cluster-point fuck. ;-)
> > > Topologically yours,
> > > Jim
> >
> > Just so we're clear uncountable sets are NOT countable. I can "count"
> > an infinite set in the sense that I can keep going and going - there is
> > always an action that will eventually get me to any member of the set.
> > However for uncountable sets no such action exists, and it's this
> > action that we call "counting".
> >
> > As for the numbers between 0 and 1 being called c that is true, and
> > the question of "does c = alph_1?" depends on your acceptance or
> > rejection of the continuum hypothesis.
> >
> > Are you familar with Cantor's first arguement for the uncountability of
> > the reals? It avoids some of the sticky points of diagonlization that
> > so many cranks get caught up on. You can check it out here.
> >
> > http://en.wikipedia.org/wiki/Cantor%27s_first_uncountability_proof

Date: 11 Dec 2006 10:41:20
From: Grip
Subject: Re: Math question: 1+1=???

Hey are you the screenplay Jim Mercurio? I was at a workshop of your
in Abq a couple of years back. Good stuff man.

G

Jim Mercurio wrote:
> I was playing with semantics. If the cardinality of that uncountable
> set is c, then we have just found a way to "count" it.
>
> Back to pot odds, implied odds, effective odds and Steve Dannenman's
> home game for me.
>
> Jim
>
>
> abe.buckingham@gmail.com wrote:
> > Jim Mercurio wrote:
> > > >
> > > > I was with you up to here. But by what definition of "countable" are the
> > > > real numbers between 0 and 1 countable? The Cantor diagonalization
> > > > argument demonstrates that any attempt to list the elements of this set is
> > > > doomed to fail. So do you have a different definition of "countable" in
> > > > mind? Just wondering.
> > > >
> > > >
> > >
> > > I was playing with semantics. "uncountable" doesn't mean not
> > > countable. They have name they give to the "infinity" of "how many
> > > real numbers between 0 and 1, right? Isn't that C. So they do count
> > > the set, but it happens to be an uncountable set by the definition that
> > > it can't be put into a 1-1 mapping of the integers.
> > >
> > > This whole topic is a cluster-point fuck. ;-)
> > > Topologically yours,
> > > Jim
> >
> > Just so we're clear uncountable sets are NOT countable. I can "count"
> > an infinite set in the sense that I can keep going and going - there is
> > always an action that will eventually get me to any member of the set.
> > However for uncountable sets no such action exists, and it's this
> > action that we call "counting".
> >
> > As for the numbers between 0 and 1 being called c that is true, and
> > the question of "does c = alph_1?" depends on your acceptance or
> > rejection of the continuum hypothesis.
> >
> > Are you familar with Cantor's first arguement for the uncountability of
> > the reals? It avoids some of the sticky points of diagonlization that
> > so many cranks get caught up on. You can check it out here.
> >
> > http://en.wikipedia.org/wiki/Cantor%27s_first_uncountability_proof

Date: 15 Dec 2006 18:51:41
From: Jim Mercurio
Subject: Re: Math question: 1+1=???

Yes, that is me.
I am the David Sklansky of that world but a fish in this one.

Grip wrote:
> Hey are you the screenplay Jim Mercurio? I was at a workshop of yours
> in Abq a couple of years back. Good stuff man.
>
> G
>
>
>
> Jim Mercurio wrote:
> > I was playing with semantics. If the cardinality of that uncountable
> > set is c, then we have just found a way to "count" it.
> >
> > Back to pot odds, implied odds, effective odds and Steve Dannenman's
> > home game for me.
> >
> > Jim
> >
> >
> > abe.buckingham@gmail.com wrote:
> > > Jim Mercurio wrote:
> > > > >
> > > > > I was with you up to here. But by what definition of "countable" are the
> > > > > real numbers between 0 and 1 countable? The Cantor diagonalization
> > > > > argument demonstrates that any attempt to list the elements of this set is
> > > > > doomed to fail. So do you have a different definition of "countable" in
> > > > > mind? Just wondering.
> > > > >
> > > > >
> > > >
> > > > I was playing with semantics. "uncountable" doesn't mean not
> > > > countable. They have name they give to the "infinity" of "how many
> > > > real numbers between 0 and 1, right? Isn't that C. So they do count
> > > > the set, but it happens to be an uncountable set by the definition that
> > > > it can't be put into a 1-1 mapping of the integers.
> > > >
> > > > This whole topic is a cluster-point fuck. ;-)
> > > > Topologically yours,
> > > > Jim
> > >
> > > Just so we're clear uncountable sets are NOT countable. I can "count"
> > > an infinite set in the sense that I can keep going and going - there is
> > > always an action that will eventually get me to any member of the set.
> > > However for uncountable sets no such action exists, and it's this
> > > action that we call "counting".
> > >
> > > As for the numbers between 0 and 1 being called c that is true, and
> > > the question of "does c = alph_1?" depends on your acceptance or
> > > rejection of the continuum hypothesis.
> > >
> > > Are you familar with Cantor's first arguement for the uncountability of
> > > the reals? It avoids some of the sticky points of diagonlization that
> > > so many cranks get caught up on. You can check it out here.
> > >
> > > http://en.wikipedia.org/wiki/Cantor%27s_first_uncountability_proof

Date: 07 Dec 2006 16:03:55
From: kurtissimo
Subject: Re: Math question: 1+1=???

Actually, 1+1=1.999999999999............ (where the 9 repeats indefinitely)

On Dec 6 2006 8:26 PM, XaQ Morphy wrote:

> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!
>
> Morphy
> http://donkeymanifesto.blogspot.com

--------
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Date: 07 Dec 2006 22:50:43
From: Palooka
Subject: Re: Math question: 1+1=???

"XaQ Morphy" <a1c5905@webnntp.invalid > wrote in message
news:ql3k44xps2.ln2@recgroups.com...
> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!
>
The troll-o-meter would have rated this very highly indeed, but somewhere in
the thread you responded to something. This surely breaches the best
traditions, n'est ce pas?

;-)

Palooka

Date: 07 Dec 2006 15:52:24
From: XaQ Morphy
Subject: Re: Math question: 1+1=???

> The troll-o-meter would have rated this very highly indeed, but somewhere in
> the thread you responded to something. This surely breaches the best
> traditions, n'est ce pas?

Why, whatever do you mean?

[18:21] thenutlow: its always the most basic simplistic fucking threads in
the world that get the most replies
[18:23] thenutlow: the thread "OT: What is one plus one?"
[18:23] thenutlow: would get 400 replies
[18:23] XaQ Morphy: lol
[18:24] XaQ Morphy: that gives me an idea

Morphy
http://donkeymanifesto.blogspot.com

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: the next generation of web-newsreaders : http://www.recgroups.com

Date: 08 Dec 18:15:30
From: CHarrison100
Subject: Re: Math question: 1+1=???

On Dec 6 2006 7:26 PM, XaQ Morphy wrote:

> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!
>
> Morphy
> http://donkeymanifesto.blogspot.com/

or the kids riddle of 1+1=11 where it would read "What is one and one?"

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Date: 08 Dec 2006 09:03:29
From: Eddie Grove
Subject: Re: Math question: 1+1=???

"XaQ Morphy" <a1c5905@webnntp.invalid > writes:

> Please help me settle an argument with a friend. There's money and pride
> involved. He's claiming there are certain mathematical instances where
> 1+1 would not equal 2. I insist that there's no way it cannot be 2. I'm
> not a math genius, so I'm looking for help. Thanks!

It depends upon your definition of 2. I think the right definition of
2 in any ring(*) is 1+1, but some people would say that 2 is undefined
for example in mod2 arithmetic.

Examples where 1+1 = 1 or 1+1 = 0 do not contradict your claim, since
in those cases you have 1+1 = 1 = 2 or 1+1 = 0 = 2. If 2 is defined,
you win. The only question is whether 2 is defined.

(*) A ring is a mathematical abstraction describing a situation in
which there is addition.

Eddie

Date: 08 Dec 2006 17:45:29
From: XaQ Morphy
Subject: Math Question Part 2: does 0.999~ = 1?

Ok, alright. I got owned in that bet. Thanks to all that replied, and I
really appreciate it. The friend I have a bet with is not an RGPer, so I
decided to use the collective math brain that is RGP to help me out here.
He offered another bet, and I just smell another sucker bet here, but
since I'm a math doofus, I need your help. He's insisting that .999~ = 1.
Here's the proof that he gave:

Proof 1:
1/3 = .333333...
2/3 = .666666...
1/3 + 2/3 = .999999... = 1.

Proof 2:
x = 0.9999...
10x = 9.9999...
10x - x = 9.9999... - 0.9999...
9x = 9
x = 1.

I'm a musician ffs, so this is foreign to me. It looks like it makes
sense, but I can't imagine this being anything close to accurate. Do you
guys agree/disagree? Help, please!

Morphy
http://donkeymanifesto.blogspot.com

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Date: 08 Dec 2006 22:44:25
From: kurtissimo
Subject: Re: Math Question Part 2: does 0.999~ = 1?

On Dec 8 2006 9:45 PM, XaQ Morphy wrote:

> Proof 1:
> 1/3 = .333333...
> 2/3 = .666666...
> 1/3 + 2/3 = .999999... = 1.

But why do you believe 1/3 = 0.33333....? Because it looks that way on a
calculator?
This is no more or less "controversial" than the claim 0.99999.... = 1.

> Proof 2:
> x = 0.9999...
> 10x = 9.9999...
> 10x - x = 9.9999... - 0.9999...
> 9x = 9
> x = 1.

This is a nice *summary* of a valid mathematical argument, but it has its
limits (pun intended).
If you're sufficiently careless with this type of argument, you can prove
things that are impossible. (Which is always fun, of course.)
For example.....

Let's say x = 9 + 90 + 900 + 9000 + 90000 + ...
Then, 10x = 90 + 900 + 9000 + 90000 + ...
Notice that x and 10x consist of all the same terms, except for the first
"9" in the sum for x.
Therefore, x - 10x = 9.
-9x = 9
x = -1
Thus 9 + 90 + 900 + 9000 + 90000 + ... = -1.

Fun stuff. So, what's wrong with this argument?

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Date: 08 Dec 2006 22:55:27
From: Erik Max Francis
Subject: Re: Math Question Part 2: does 0.999~ = 1?

kurtissimo wrote:

> But why do you believe 1/3 = 0.33333....? Because it looks that way on a
> calculator?
> This is no more or less "controversial" than the claim 0.99999.... = 1.

It's no more or less "controversial" because it's true. That 0.333... =
1 is not only true, but it's a fact every sixth grader knows.

> This is a nice *summary* of a valid mathematical argument, but it has its
> limits (pun intended).
> If you're sufficiently careless with this type of argument, you can prove
> things that are impossible. (Which is always fun, of course.)
> For example.....
>
> Let's say x = 9 + 90 + 900 + 9000 + 90000 + ...
> Then, 10x = 90 + 900 + 9000 + 90000 + ...
> Notice that x and 10x consist of all the same terms, except for the first
> "9" in the sum for x.
> Therefore, x - 10x = 9.
> -9x = 9
> x = -1
> Thus 9 + 90 + 900 + 9000 + 90000 + ... = -1.
>
> Fun stuff. So, what's wrong with this argument?

The expression of x is an infinite series which does not converge, and
since infinity is not a number, the first line is nonsensical. One can
only speak of infinity in limits. The first mistake in a proof renders
the rest of it invalid.

--
Erik Max Francis && max@alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM, Y!M erikmaxfrancis
Woman was God's _second_ mistake.
-- Friedrich Nietzsche

Date: 08 Dec 2006 23:57:39
From: eleaticus
Subject: Re: Math Question Part 2: does 0.999~ = 1?

"XaQ Morphy" <a1c5905@webnntp.invalid > wrote in message
news:p2hp44xe0c.ln2@recgroups.com...
> Ok, alright. I got owned in that bet. Thanks to all that replied, and I
> really appreciate it. The friend I have a bet with is not an RGPer, so I
> decided to use the collective math brain that is RGP to help me out here.
> He offered another bet, and I just smell another sucker bet here, but
> since I'm a math doofus, I need your help. He's insisting that .999~ = 1.
> Here's the proof that he gave:

That is proof that .999~=1 in exactly the same the more shizoid mathers
'prove' that Zeno's basic continuous-base paradox is 'proved' solved: by
limits; the limit of the sum of halves remainders of halves of remainders
of halves or remainders ... is the whole.

Which begs the quuestion: what is the limit of the sums of the other form of
the paradox: you can't half way because first you have to go half that
distance but first you have to go half that distance ...

Answer: zero.

IE, if time and space physically exist and are continuous (infinitely
divisible) the forward tip of an object can't get there, anywhere.

--
eleaticus
ee-lee-AT-i-cus
eleaticus@bellsouth.net

Date: 08 Dec 2006 22:14:38
From: Erik Max Francis
Subject: Re: Math Question Part 2: does 0.999~ = 1?

eleaticus wrote:

> Which begs the quuestion: what is the limit of the sums of the other form of
> the paradox: you can't half way because first you have to go half that
> distance but first you have to go half that distance ...
>
> Answer: zero.
>
> IE, if time and space physically exist and are continuous (infinitely
> divisible) the forward tip of an object can't get there, anywhere.

All this example does is play games with motion. You can certainly
express the (finite) distance between two points A and B as an infinite
series. But the limit of the series converges, so it's a finite
distance even if you divide it up into an infinite number of partitions.

With a finite distance, and a finite speed, the time it takes to cross
is finite, no matter how you divide it up. Calculus _helps_ analyze
continuous motion; it doesn't hinder it.

--
Erik Max Francis && max@alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM, Y!M erikmaxfrancis
Woman was God's _second_ mistake.
-- Friedrich Nietzsche

Date: 09 Dec 2006 00:27:29
From: eleaticus
Subject: Re: Math Question Part 2: does 0.999~ = 1?

"Erik Max Francis" <max@alcyone.com > wrote in message
news:JaGdndJjEYHEyefYnZ2dnUVZ_qjinZ2d@speakeasy.net...
> eleaticus wrote:
>
> > Which begs the quuestion: what is the limit of the sums of the other
form of
> > the paradox: you can't half way because first you have to go half that
> > distance but first you have to go half that distance ...
> >
> > Answer: zero.
> >
> > IE, if time and space physically exist and are continuous (infinitely
> > divisible) the forward tip of an object can't get there, anywhere.
>
> All this example does is play games with motion. You can certainly
> express the (finite) distance between two points A and B as an infinite
> series. But the limit of the series converges, so it's a finite
> distance even if you divide it up into an infinite number of partitions.
>
> With a finite distance, and a finite speed, the time it takes to cross
> is finite, no matter how you divide it up. Calculus _helps_ analyze
> continuous motion; it doesn't hinder it.

Which misses the point. As well as being idiocy.

When you wish to refute the claim for a process - a sequence over time - you
(if honest and not stupid) honor and model the process, not a fait accompli.

First you show the process as given can be completed, THEN you make claims
as to what the sum of the process is. You want to say what the sum would be,
then have at it.

By the way, it does not play games with motion, it questions the ideas of
continuous time and space.

Deal with it.

No don't.

You have already proved incapable psychologically of abstact thought.
--
eleaticus
ee-lee-AT-i-cus
eleaticus@bellsouth.net

Date: 12 Dec 2006 21:45:50
From: Andrew.Sliversalts
Subject: Re: Math Question Part 2: does 0.999~ = 1?

Costing the net hundreds if not thousands of dollars, eleaticus said:
>
>
> IE, if time and space physically exist and are continuous (infinitely
> divisible) the forward tip of an object can't get there, anywhere.

Time doesn't exist

Date: 09 Dec 2006 04:22:35
From: Palooka
Subject: Re: Math Question Part 2: does 0.999~ = 1?

"XaQ Morphy" <a1c5905@webnntp.invalid > wrote in message
news:p2hp44xe0c.ln2@recgroups.com...
> Ok, alright. I got owned in that bet. Thanks to all that replied, and I
> really appreciate it. The friend I have a bet with is not an RGPer, so I
> decided to use the collective math brain that is RGP to help me out here.
> He offered another bet, and I just smell another sucker bet here, but
> since I'm a math doofus, I need your help. He's insisting that .999~ = 1.
> Here's the proof that he gave:
>
> Proof 1:
> 1/3 = .333333...
> 2/3 = .666666...
> 1/3 + 2/3 = .999999... = 1.
>
> Proof 2:
> x = 0.9999...
> 10x = 9.9999...
> 10x - x = 9.9999... - 0.9999...
> 9x = 9
> x = 1.
>
> I'm a musician ffs, so this is foreign to me. It looks like it makes
> sense, but I can't imagine this being anything close to accurate. Do you
> guys agree/disagree? Help, please!
>
So 1 + 1 < 400? Good try, though.

:-)
Palooka

Date: 08 Dec 2006 19:21:59
From: Erik Max Francis
Subject: Re: Math Question Part 2: does 0.999~ = 1?

XaQ Morphy wrote:

> Ok, alright. I got owned in that bet. Thanks to all that replied, and I
> really appreciate it. The friend I have a bet with is not an RGPer, so I
> decided to use the collective math brain that is RGP to help me out here.
> He offered another bet, and I just smell another sucker bet here, but
> since I'm a math doofus, I need your help. He's insisting that .999~ = 1.

Yes. 0.999... does in fact equal 1.

Neither proof he gives is rigorous to the point of pleasing a
mathematician, but the logic used in both are correct and legitimate. A
real proof involves the limit of an infinite series, and that limit does
equal 1.

--
Erik Max Francis && max@alcyone.com && http://www.alcyone.com/max/
San Jose, CA, USA && 37 20 N 121 53 W && AIM, Y!M erikmaxfrancis
Sometimes there's no point in giving up.
-- Louis Wu

Date: 08 Dec 2006 20:52:54
From:
Subject: Re: Math Question Part 2: does 0.999~ = 1?

Gary Carson wrote:
> On Dec 8 2006 9:22 PM, Erik Max Francis wrote:
>
> > XaQ Morphy wrote:
> >
> > > Ok, alright. I got owned in that bet. Thanks to all that replied, and I
> > > really appreciate it. The friend I have a bet with is not an RGPer, so I
> > > decided to use the collective math brain that is RGP to help me out here.
> > > He offered another bet, and I just smell another sucker bet here, but
> > > since I'm a math doofus, I need your help. He's insisting that .999~ = 1.
> >
> > Yes. 0.999... does in fact equal 1.
> >
> > Neither proof he gives is rigorous to the point of pleasing a
> > mathematician, but the logic used in both are correct and legitimate. A
> > real proof involves the limit of an infinite series, and that limit does
> > equal 1.
>
> So correct and legitimate logic isn't good enough for a mathematician? Do they
> require the use of special magic dust for sale only in the gift shop at
> Princeton?
> >

He probably should simply said that it was incomplete, you first have
to define what 0.999~ actually is and then what the proper equivilence
relation so that 0.999~ = 1 and then prove that objects like 0.999~
form a field. Once that's done you can use the arguements to show that
0.999~ = 1, but at this point it would be a specific example of a more
general result. The arguements given without this background put the
cart before the horse.

Date: 09 Dec
From: Gary Carson
Subject: Re: Math Question Part 2: does 0.999~ = 1?

On Dec 8 2006 10:52 PM, abe.buckingham@gmail.com wrote:

> Gary Carson wrote:
> > On Dec 8 2006 9:22 PM, Erik Max Francis wrote:
> >
> > > XaQ Morphy wrote:
> > >
> > > > Ok, alright. I got owned in that bet. Thanks to all that replied, and I
> > > > really appreciate it. The friend I have a bet with is not an RGPer, so I
> > > > decided to use the collective math brain that is RGP to help me out
> > > > here.
> > > > He offered another bet, and I just smell another sucker bet here, but
> > > > since I'm a math doofus, I need your help. He's insisting that .999~ =
> > > > 1.
> > >
> > > Yes. 0.999... does in fact equal 1.
> > >
> > > Neither proof he gives is rigorous to the point of pleasing a
> > > mathematician, but the logic used in both are correct and legitimate. A
> > > real proof involves the limit of an infinite series, and that limit does
> > > equal 1.
> >
> > So correct and legitimate logic isn't good enough for a mathematician? Do
> > they
> > require the use of special magic dust for sale only in the gift shop at
> > Princeton?
> > >
>
> He probably should simply said that it was incomplete, you first have
> to define what 0.999~ actually is and then what the proper equivilence
> relation so that 0.999~ = 1 and then prove that objects like 0.999~
> form a field. Once that's done you can use the arguements to show that
> 0.999~ = 1, but at this point it would be a specific example of a more
> general result. The arguements given without this background put the
> cart before the horse.

Yes, if you want to prove A=B you need to define A, define B, and define =. I
guess you'll also need to define define. And then use that magic dust from the
Princeton gift shop.

The only reason you have to bring up anything about a field is that way you can
pretend the result is out of reach of the typical math literate person and
you're special because you can use words you don't need to use.

So we'll just jump ahead and accept the premise that you're special.

Gary Carson
http://www.garycarson.com

_______________________________________________________________
Posted using RecPoker.com v2.2 - http://www.recpoker.com

Date: 09 Dec 2006 05:56:32
From:
Subject: Re: Math Question Part 2: does 0.999~ = 1?

Gary Carson wrote:
> On Dec 8 2006 10:52 PM, abe.buckingham@gmail.com wrote:
>
> > Gary Carson wrote:
> > > On Dec 8 2006 9:22 PM, Erik Max Francis wrote:
> > >
> > > > XaQ Morphy wrote:
> > > >
> > > > > Ok, alright. I got owned in that bet. Thanks to all that replied, and I
> > > > > really appreciate it. The friend I have a bet with is not an RGPer, so I
> > > > > decided to use the collective math brain that is RGP to help me out
> > > > > here.
> > > > > He offered another bet, and I just smell another sucker bet here, but
> > > > > since I'm a math doofus, I need your help. He's insisting that .999~ =
> > > > > 1.
> > > >
> > > > Yes. 0.999... does in fact equal 1.
> > > >
> > > > Neither proof he gives is rigorous to the point of pleasing a
> > > > mathematician, but the logic used in both are correct and legitimate. A
> > > > real proof involves the limit of an infinite series, and that limit does
> > > > equal 1.
> > >
> > > So correct and legitimate logic isn't good enough for a mathematician? Do
> > > they
> > > require the use of special magic dust for sale only in the gift shop at
> > > Princeton?
> > > >
> >
> > He probably should simply said that it was incomplete, you first have
> > to define what 0.999~ actually is and then what the proper equivilence
> > relation so that 0.999~ = 1 and then prove that objects like 0.999~
> > form a field. Once that's done you can use the arguements to show that
> > 0.999~ = 1, but at this point it would be a specific example of a more
> > general result. The arguements given without this background put the
> > cart before the horse.
>
> Yes, if you want to prove A=B you need to define A, define B, and define =. I
> guess you'll also need to define define. And then use that magic dust from the
> Princeton gift shop.
>
> The only reason you have to bring up anything about a field is that way you can
> pretend the result is out of reach of the typical math literate person and
> you're special because you can use words you don't need to use.
>
> So we'll just jump ahead and accept the premise that you're special.
>
> Gary Carson
> http://www.garycarson.com
>

I realize you don't know much about math, but my posts are for those
who do and take an interest in it, if you can't undertand them (which
any math literate person using google can) then ignore them. Or do you
take pride in being an ass?

Date: 09 Dec
From: Gary Carson
Subject: Re: Math Question Part 2: does 0.999~ = 1?

On Dec 8 2006 9:22 PM, Erik Max Francis wrote:

> XaQ Morphy wrote:
>
> > Ok, alright. I got owned in that bet. Thanks to all that replied, and I
> > really appreciate it. The friend I have a bet with is not an RGPer, so I
> > decided to use the collective math brain that is RGP to help me out here.
> > He offered another bet, and I just smell another sucker bet here, but
> > since I'm a math doofus, I need your help. He's insisting that .999~ = 1.
>
> Yes. 0.999... does in fact equal 1.
>
> Neither proof he gives is rigorous to the point of pleasing a
> mathematician, but the logic used in both are correct and legitimate. A
> real proof involves the limit of an infinite series, and that limit does
> equal 1.

So correct and legitimate logic isn't good enough for a mathematician? Do they
require the use of special magic dust for sale only in the gift shop at
Princeton?
>
> --
> Erik Max Francis && max@alcyone.com && http://www.alcyone.com/max/
> San Jose, CA, USA && 37 20 N 121 53 W && AIM, Y!M erikmaxfrancis
> Sometimes there's no point in giving up.
> -- Louis Wu
Gary Carson
http://www.garycarson.com

_______________________________________________________________
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Date: 08 Dec 2006 19:14:51
From: Eddie Grove
Subject: Re: Math Question Part 2: does 0.999~ = 1?

"XaQ Morphy" <a1c5905@webnntp.invalid > writes:

> Ok, alright. I got owned in that bet. Thanks to all that replied, and I
> really appreciate it. The friend I have a bet with is not an RGPer, so I
> decided to use the collective math brain that is RGP to help me out here.
> He offered another bet, and I just smell another sucker bet here, but
> since I'm a math doofus, I need your help. He's insisting that .999~ = 1.
> Here's the proof that he gave:
>
> Proof 1:
> 1/3 = .333333...
> 2/3 = .666666...
> 1/3 + 2/3 = .999999... = 1.
>
> Proof 2:
> x = 0.9999...
> 10x = 9.9999...
> 10x - x = 9.9999... - 0.9999...
> 9x = 9
> x = 1.
>
> I'm a musician ffs, so this is foreign to me. It looks like it makes
> sense, but I can't imagine this being anything close to accurate. Do you
> guys agree/disagree? Help, please!

You have to define what .999~ means carefully, but if you do both of
his proofs are essentially correct.

Proof 1 is better in the sense that it takes extra work to get through
the formalities when you have negative terms in infinite series.

Eddie

Date: 08 Dec 2006 18:42:14
From: akqjt98
Subject: Re: Math Question Part 2: does 0.999~ = 1?

On Dec 8 2006 7:45 PM, XaQ Morphy wrote:

> Ok, alright. I got owned in that bet. Thanks to all that replied, and I
> really appreciate it. The friend I have a bet with is not an RGPer, so I
> decided to use the collective math brain that is RGP to help me out here.
> He offered another bet, and I just smell another sucker bet here, but
> since I'm a math doofus, I need your help. He's insisting that .999~ = 1.
> Here's the proof that he gave:
>
> Proof 1:
> 1/3 = .333333...
> 2/3 = .666666...
> 1/3 + 2/3 = .999999... = 1.
>
> Proof 2:
> x = 0.9999...
> 10x = 9.9999...
> 10x - x = 9.9999... - 0.9999...
> 9x = 9
> x = 1.
>
> I'm a musician ffs, so this is foreign to me. It looks like it makes
> sense, but I can't imagine this being anything close to accurate. Do you
> guys agree/disagree? Help, please!
>
> Morphy
> http://donkeymanifesto.blogspot.com

It's a rounding error ffs - there was a huge bank scandel about this in
the 70's or 80's where banks and mortgage companies were takling the
'extra' 1/4 cents and shit from people's accounts and redirecting them to
their own accounts every month. Some of these assholes got extremely rich
off this scam. but I digress...

The proof appears to work because of the rounding error, and it's all but
impossible to disprove, but it simply isn't true. If you're at a table and
you have .99999...... outs, will you ever be able to win the hand?

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Date: 08 Dec 2006 22:58:38
From: kurtissimo
Subject: Re: Math Question Part 2: does 0.999~ = 1?

On Dec 8 2006 10:42 PM, akqjt98 wrote:

> It's a rounding error ffs - there was a huge bank scandel about this in
> the 70's or 80's where banks and mortgage companies were takling the
> 'extra' 1/4 cents and shit from people's accounts and redirecting them to
> their own accounts every month. Some of these assholes got extremely rich
> off this scam. but I digress...

There was a banking scandal involving *infinite* sums? I doubt that, since
it's impossible.

I don't think you're getting the "infinite" part of this whole discussion.
There are no "rounding errors" in an infinite sum. There is no last place
from which to round up or down.

> The proof appears to work because of the rounding error, and it's all but
> impossible to disprove, but it simply isn't true. If you're at a table and
> you have .99999...... outs, will you ever be able to win the hand?

Just out of curiosity: what is the value of 1 - 0.999999.... ?
You're asserting that it's *not* zero, so I'm wondering what value you'd
assign to this difference.

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Date: 09 Dec
From: Gary Carson
Subject: Re: Math Question Part 2: does 0.999~ = 1?

On Dec 9 2006 12:58 AM, kurtissimo wrote:

> On Dec 8 2006 10:42 PM, akqjt98 wrote:
>
> > It's a rounding error ffs - there was a huge bank scandel about this in
> > the 70's or 80's where banks and mortgage companies were takling the
> > 'extra' 1/4 cents and shit from people's accounts and redirecting them to
> > their own accounts every month. Some of these assholes got extremely rich
> > off this scam. but I digress...
>
> There was a banking scandal involving *infinite* sums? I doubt that, since
> it's impossible.

He's talking about urban legends of some programmer somewhere who put all the
fractional pennies of interest payments on savings accounts into his personal
accounts.

It never happened anywhere, there was never any such scandel anywhere, but Irish
Mike and this clown got an email about it.

> Just out of curiosity: what is the value of 1 - 0.999999.... ?
> You're asserting that it's *not* zero, so I'm wondering what value you'd
> assign to this difference.

It's obvious. It's 0.00000000 ... 000001

Gary Carson
http://www.garycarson.com

_______________________________________________________________
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Date: 09 Dec 2006 09:02:33
From: akqjt98
Subject: Re: Math Question Part 2: does 0.999~ = 1?

On Dec 9 2006 1:36 AM, Gary Carson wrote:

> On Dec 9 2006 12:58 AM, kurtissimo wrote:
>
> > On Dec 8 2006 10:42 PM, akqjt98 wrote:
> >
> > > It's a rounding error ffs - there was a huge bank scandel about this in
> > > the 70's or 80's where banks and mortgage companies were takling the
> > > 'extra' 1/4 cents and shit from people's accounts and redirecting them to
> > > their own accounts every month. Some of these assholes got extremely rich
> > > off this scam. but I digress...
> >
> > There was a banking scandal involving *infinite* sums? I doubt that, since
> > it's impossible.
>
> He's talking about urban legends of some programmer somewhere who put all the
> fractional pennies of interest payments on savings accounts into his personal
> accounts.
>
> It never happened anywhere, there was never any such scandel anywhere, but
Irish
> Mike and this clown got an email about it.
>
> > Just out of curiosity: what is the value of 1 - 0.999999.... ?
> > You're asserting that it's *not* zero, so I'm wondering what value you'd
> > assign to this difference.
>
> It's obvious. It's 0.00000000 ... 000001
>
> Gary Carson
> http://www.garycarson.com

First, it's not an urban legend - nobody ever actually did it, but there
was testimony in front of congress about it and several bank reform laws
were written to allow for it. When you pay off your mortgage, you still to
this day get a small (very small) check back for the total of the myriad
fractional cents that you paid but were never credited. Look it up

And you never bothered to answer the question... if you have .9999999...
outs, will you ever win the hand?

____________________________________________________________________
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Date: 09 Dec 18:37:51
From: Gary Carson
Subject: Re: Math Question Part 2: does 0.999~ = 1?

On Dec 9 2006 11:02 AM, akqjt98 wrote:

> On Dec 9 2006 1:36 AM, Gary Carson wrote:
>
> > On Dec 9 2006 12:58 AM, kurtissimo wrote:
> >
> > > On Dec 8 2006 10:42 PM, akqjt98 wrote:
> > >
> > > > It's a rounding error ffs - there was a huge bank scandel about this in
> > > > the 70's or 80's where banks and mortgage companies were takling the
> > > > 'extra' 1/4 cents and shit from people's accounts and redirecting them
> > > > to
> > > > their own accounts every month. Some of these assholes got extremely
> > > > rich
> > > > off this scam. but I digress...
> > >
> > > There was a banking scandal involving *infinite* sums? I doubt that, since
> > > it's impossible.
> >
> > He's talking about urban legends of some programmer somewhere who put all
> > the
> > fractional pennies of interest payments on savings accounts into his
> > personal
> > accounts.
> >
> > It never happened anywhere, there was never any such scandel anywhere, but
> Irish
> > Mike and this clown got an email about it.
> >

>
> First, it's not an urban legend - nobody ever actually did it, but there
> was testimony in front of congress about it and several bank reform laws
> were written to allow for it.

Oh, gee. It can't be nonsense if some congressman said it.

> When you pay off your mortgage, you still to
> this day get a small (very small) check back for the total of the myriad
> fractional cents that you paid but were never credited. Look it up

Well, I don't need to look it up, I was there in the 70's and 80's. The legend
isn't about paying off mortages early and how that effects interest
calculations. The legend is about creating a bit bucket and the embezzlement of
fractional pennies in interest paid to savings accounts.

Interest calculations involve some projections based on the maturity of the
instrument. Paying off early is like exercising a callable bond and previous
interest calculations need to be adjusted. I'm sure many banks had it in their
mortage contracts that any such adjustments would not be rebate and congress
passed some laws outlawing such contract terms.

But loans are assets and savings accounts are liabilties and the interest isn't
calculated in the same way. For example, during the days of Regulation Q some
banks used continious compounding for interest payments which resulting in
slightly higher interest cost than daily compounding would. We did it by
calculating the continious compounding and creating an equavalnt rate for daily
compounding. We could then advertise that we paid a higher effective rate on
savings than most other banks.

You probably be surprised how many small banks didn't have anybody in their
systems groups that didn't know how to calculate yeilds. In some cases they
didn't even have anybody in their bond department who could calculated yeids.
We had a nice little business doing quarterly bond yeild reports for our smaller
correspondents.

>
> And you never bothered to answer the question... if you have .9999999...
> outs, will you ever win the hand?

Oh, I thought it was a joke. I didn't know it was a serious question. The
answer is it's a stupid question because you don't count outs on a continium.
If you counted out equivalents (which might be approximatly continious) then the
answer is yes.

If the grass was orange would the sky be white?

Gary Carson
http://www.garycarson.com

_______________________________________________________________
The Largest Online Poker Community - http://www.recpoker.com

Date: 09 Dec 2006 15:13:20
From: akqjt98
Subject: Re: Math Question Part 2: does 0.999~ = 1?

On Dec 9 2006 12:37 PM, Gary Carson wrote:

> On Dec 9 2006 11:02 AM, akqjt98 wrote:
>
> > On Dec 9 2006 1:36 AM, Gary Carson wrote:
> >
> > > On Dec 9 2006 12:58 AM, kurtissimo wrote:
> > >
> > > > On Dec 8 2006 10:42 PM, akqjt98 wrote:
> > > >
> > > > > It's a rounding error ffs - there was a huge bank scandel about this
in
> > > > > the 70's or 80's where banks and mortgage companies were takling the
> > > > > 'extra' 1/4 cents and shit from people's accounts and redirecting
them
> > > > > to
> > > > > their own accounts every month. Some of these assholes got extremely
> > > > > rich
> > > > > off this scam. but I digress...
> > > >
> > > > There was a banking scandal involving *infinite* sums? I doubt that,
since
> > > > it's impossible.
> > >
> > > He's talking about urban legends of some programmer somewhere who put all
> > > the
> > > fractional pennies of interest payments on savings accounts into his
> > > personal
> > > accounts.
> > >
> > > It never happened anywhere, there was never any such scandel anywhere,
but
> > Irish
> > > Mike and this clown got an email about it.
> > >
>
> >
> > First, it's not an urban legend - nobody ever actually did it, but there
> > was testimony in front of congress about it and several bank reform laws
> > were written to allow for it.
>
> Oh, gee. It can't be nonsense if some congressman said it.
>
> > When you pay off your mortgage, you still to
> > this day get a small (very small) check back for the total of the myriad
> > fractional cents that you paid but were never credited. Look it up
>
> Well, I don't need to look it up, I was there in the 70's and 80's. The
legend
> isn't about paying off mortages early and how that effects interest
> calculations. The legend is about creating a bit bucket and the
embezzlement of
> fractional pennies in interest paid to savings accounts.
>
> Interest calculations involve some projections based on the maturity of the
> instrument. Paying off early is like exercising a callable bond and previous
> interest calculations need to be adjusted. I'm sure many banks had it in
their
> mortage contracts that any such adjustments would not be rebate and congress
> passed some laws outlawing such contract terms.
>
> But loans are assets and savings accounts are liabilties and the interest
isn't
> calculated in the same way. For example, during the days of Regulation Q
some
> banks used continious compounding for interest payments which resulting in
> slightly higher interest cost than daily compounding would. We did it by
> calculating the continious compounding and creating an equavalnt rate for
daily
> compounding. We could then advertise that we paid a higher effective rate on
> savings than most other banks.
>
> You probably be surprised how many small banks didn't have anybody in their
> systems groups that didn't know how to calculate yeilds. In some cases they
> didn't even have anybody in their bond department who could calculated
yeids.
> We had a nice little business doing quarterly bond yeild reports for our
smaller
> correspondents.
>
> >
> > And you never bothered to answer the question... if you have .9999999...
> > outs, will you ever win the hand?
>
> Oh, I thought it was a joke. I didn't know it was a serious question. The
> answer is it's a stupid question because you don't count outs on a
continium.
> If you counted out equivalents (which might be approximatly continious) then
the
> answer is yes.
>
> If the grass was orange would the sky be white?
>
> Gary Carson
> http://www.garycarson.com

I was also 'there in the 70s and 80s' and also happen to know one of the
gentlemen who testified in front of congress. The deal was that lenders
were making a shitload of extra money because they weren't paying back
these accumulated fractional amounts - the law forced them to do so. I
don't remember all the exact details, but it was something to do with
money they weren't entitled to...

..and no, the sky would not be white. The sky has no color - it appears
to be blue due to the refraction of light rays thru the atmosphere, but in
fact it has no color at all. To quote some stupid soft drink commercial,
"...never had it, never will"

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Date: 09 Dec 23:29:43
From: Gary Carson
Subject: Re: Math Question Part 2: does 0.999~ = 1?

> I was also 'there in the 70s and 80s' and also happen to know one of the
> gentlemen who testified in front of congress. The deal was that lenders
> were making a shitload of extra money because they weren't paying back
> these accumulated fractional amounts - the law forced them to do so. I
> don't remember all the exact details, but it was something to do with
> money they weren't entitled to...

It wasn't fraud. And it wasn't about round off of interest payments. It was
money that they were contractually entitled to. But some nutcases decided that
such loan contracts were morally wrong and passed a law outlawing it. Nobody in
banking really much gave a shit about it. The objection from the banking
community wasn't about the money, it was about having to recalculate based on a
change in term was just a pain in the ass.

The urban legend being discussed was about truncating interest payments on
savings accounts and emplyees stealing the roundoff.

Any such attempt would immediately be caught by any bank that did double entry
bookkeeping.

>
> ...and no, the sky would not be white. The sky has no color - it appears
> to be blue due to the refraction of light rays thru the atmosphere, but in
> fact it has no color at all. To quote some stupid soft drink commercial,
> "...never had it, never will"

Uh. I think refraction of light rays is what color is. Whether it's the color
of the sky or the color of your car doesn't really matter.

But I might be mistaken about that. I havn't really read much about color since
about the 8th grade.

Gary Carson
http://www.garycarson.com

_______________________________________________________________
The Largest Online Poker Community - http://www.recpoker.com

Date: 09 Dec 2006 00:18:09
From: kurtissimo
Subject: Re: Math Question Part 2: does 0.999~ = 1?

On Dec 9 2006 3:36 AM, Gary Carson wrote:
> On Dec 9 2006 12:58 AM, kurtissimo wrote:
> > Just out of curiosity: what is the value of 1 - 0.999999.... ?
>
> It's obvious. It's 0.00000000 ... 000001

Oh, that's right - I forgot about the option of putting a 1 in the
infinity-plus-oneth decimal place. How foolish of me.

I should have realized this was the idea; after all, every high school
student in America knows that 2/3 = .6666...66667, where that 7 is in the
infinity-plus-oneth place. ....or is it the infinityth place? I get
confused by all this higher math...

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Date: 09 Dec
From: Gary Carson
Subject: Re: Math Question Part 2: does 0.999~ = 1?

On Dec 9 2006 2:18 AM, kurtissimo wrote:

> On Dec 9 2006 3:36 AM, Gary Carson wrote:
> > On Dec 9 2006 12:58 AM, kurtissimo wrote:
> > > Just out of curiosity: what is the value of 1 - 0.999999.... ?
> >
> > It's obvious. It's 0.00000000 ... 000001
>
> Oh, that's right - I forgot about the option of putting a 1 in the
> infinity-plus-oneth decimal place. How foolish of me.
>
> I should have realized this was the idea; after all, every high school
> student in America knows that 2/3 = .6666...66667, where that 7 is in the
> infinity-plus-oneth place. ....or is it the infinityth place? I get
> confused by all this higher math...

I'm going to write a computer program to add together a .666666 ... 6667 with
the 7 in the infinitith place with one with the 7 in the infinitigh -1 place.
I'll let it run overnight and report the result in the morning.

Did you read about he English high school math teacher who claims that he's
solved the problem of division by zero. Rather than treat it as undefined he
says to treat it as nan (not a number) and everything works out just find.

He's serious.
Gary Carson
http://www.garycarson.com

_______________________________________________________________
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Date: 09 Dec
From: Gary Carson
Subject: Re: Math Question Part 2: does 0.999~ = 1?

When you start dealing with things like infinity and continouity you will have
things that don't quite seem right, but they are.

The reason for that is that is that infinity isn't really a number in the sense
it's not a Real Number. You can't do arithmetic with infinity. If you could
then you'd have 1-infinity = intinity so subtracting infinity from both sides
gives you 1=0.

Also continious numbers means you can't represent all numbers with unique
sequences of digits. If you could then they aren't continious.

so .99999... is equal to 1 but that's just a definciency in trying to use
discrete digits to represent continious numbers.

Just don't take the other guys prop bet and you'll never go wrong.

On Dec 8 2006 7:45 PM, XaQ Morphy wrote:

> Ok, alright. I got owned in that bet. Thanks to all that replied, and I
> really appreciate it. The friend I have a bet with is not an RGPer, so I
> decided to use the collective math brain that is RGP to help me out here.
> He offered another bet, and I just smell another sucker bet here, but
> since I'm a math doofus, I need your help. He's insisting that .999~ = 1.
> Here's the proof that he gave:
>
> Proof 1:
> 1/3 = .333333...
> 2/3 = .666666...
> 1/3 + 2/3 = .999999... = 1.
>
> Proof 2:
> x = 0.9999...
> 10x = 9.9999...
> 10x - x = 9.9999... - 0.9999...
> 9x = 9
> x = 1.
>
> I'm a musician ffs, so this is foreign to me. It looks like it makes
> sense, but I can't imagine this being anything close to accurate. Do you
> guys agree/disagree? Help, please!
>
> Morphy
> http://donkeymanifesto.blogspot.com/
Gary Carson
http://www.garycarson.com

_______________________________________________________________
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Date: 09 Dec 2006 07:54:04
From: Keith Willoughby
Subject: Re: Math Question Part 2: does 0.999~ = 1?

"akqjt98" <a59933d@webnntp.invalid > writes:

> It's a rounding error ffs - there was a huge bank scandel about this
> in the 70's or 80's where banks and mortgage companies were takling
> the 'extra' 1/4 cents and shit from people's accounts and redirecting
> them to their own accounts every month. Some of these assholes got
> extremely rich off this scam. but I digress...

That's the plot of Superman III.

There's a great bit in Office Space, where one of the protagonists is
suggesting doing this very thing. I'm thinking, 'they stole this plot
from Superman III', and then one of the other protagonists says 'Hey,
didn't they do this in Superman III?'

--
Keith Willoughby http://flat222.org/keith/
"I'm Slim Shady, the Real Slim Shady
The other Slim Shady's gone to play tennis"

Date: 11 Dec 2006 08:32:06
From: XaQ Morphy
Subject: Re: Math question: Conclusion

Well, I'm a bit disappointed. When this challenge was originally talked
about, the number of 400 posts was thrown out. While I was sure it would
never hit 400, I was pretty sure the nits on RGP would get at least 100
posts out of a thread. I mean ffs people, if you can talk about nothing
but rampaging for weeks even after told that it was started out as a joke,
surely you can come up with 100 posts debating whether or not 1+1=2!

I'm disappointed.

Morphy
http://donkeymanifesto.blogspot.com

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Date: 11 Dec 2006 18:27:33
From: Palooka
Subject: Re: Math question: Conclusion

"XaQ Morphy" <a1c5905@webnntp.invalid > wrote in message
news:6pd054xdtv.ln2@recgroups.com...
> Well, I'm a bit disappointed. When this challenge was originally talked
> about, the number of 400 posts was thrown out. While I was sure it would
> never hit 400, I was pretty sure the nits on RGP would get at least 100
> posts out of a thread. I mean ffs people, if you can talk about nothing
> but rampaging for weeks even after told that it was started out as a joke,
> surely you can come up with 100 posts debating whether or not 1+1=2!
>
> I'm disappointed.
>
> Morphy
> http://donkeymanifesto.blogspot.com
>
I still think it was a jolly good effort. No need to be discouraged, but
please do NOT start a thread debating whether or not 0.002 = 0.00002.

:-)
Palooka

Date: 11 Dec 2006 10:29:02
From: XaQ Morphy
Subject: Re: Math question: Conclusion

> I still think it was a jolly good effort. No need to be discouraged, but
> please do NOT start a thread debating whether or not 0.002 = 0.00002.

It was

Date: 12 Dec 2006 21:46:51
From: Andrew.Sliversalts
Subject: Re: Math question: Conclusion

Costing the net hundreds if not thousands of dollars, XaQ Morphy said:
> 1+1=2!

Don't start dragging factorials into it, ffs.