A is not A

[ComradeRed]

Before we begin, allow me to just say I don't mix philosophy and politics togather unlike some phil-itics (like objectivism) so don't hammer away at me in political discussion; afterall, most of the time I just play the devils advocate in philosophical discussion.

Lemme begin. A=A, right? Self explanatory. However, could it be possible that A is not A? Absolutely! Take Shrodigner's cat for example! Or math:
1. 1 divided by infinity=2 divided by infinity (GIVEN)
2. 1 (infinity)=2 (infinity) (mulitplication property of equality)
3. 1=2 (division property of equality)

Therefore A is not A, if 1=2.

Remember: I am just the devil's advocate!

[Mulkaccino]

Hmmm, not sure, but I don't think you cannot use infinity like that. Your treating it as a undefined variable, when it's actually a fixed number. It's just an undefined fixed.

1. 1 divided by cosmictoasteroven=2 divided by cosmictoasteroven (GIVEN)
2. 1 (cosmictoasteroven)=2 (cosmictoasteroven) (mulitplication property of equality)
3. 1=2 (division property of equality)

[orgaelin]

LOL @ Mulkaccino - and very true!

[ComradeRed]

Hmmm, not sure, but I don't think you cannot use infinity like that. Your treating it as a undefined variable, when it's actually a fixed number. It's just an undefined fixed.

I beg to differ, infinity is an idea not a fixed number! It really is a variable, since it varies, always getting bigger! Check it at wikipedia!

[Mulkaccino]

Thanks comrade, wasn't certain on that. BUT (and I'm not a math major), since infinity is consistantly getting bigger, you could say that it's a variable "with an agenda." I can't imagine you could treat it the same as variable X, which does not have an agenda (X could be anything, it doesn't have to get bigger). Furthermore, X can be defined, infinity cannot be defined. X can equal 2, X=2. Can infinity equal 2? Infinity=2? Does that mean those who say god is infinite are actually saying god could equal 2??? Or that the edge of the universe can be defined as the number 2??? I really don't think infinity can be used in your equation like you used it.

Excuse me while I put my brain in a black-hole...

[ComradeRed]

The point is, however, that it is a variable that is not equal to zero. It doesn't matter what it is equal to, just not zero! And fundementally, IT'S TRUE! That's why I used it!

[5010]

OK, let's take a closer look at infinity...

Every horse has an infinite number of legs. (Proof by intimidation.)

Proof. Horses have an even number of legs. Behind they have two legs and in front they have fore legs. This makes six legs, which is certainly an odd number of legs for a horse. But the only number that is both odd and even is infinity. Therefore horses have an infinite number of legs.

Now let's take a closer look at equality...

What is the difference between a Psychotic, a Neurotic and a mathematician? A Psychotic believes that 2+2=5. A Neurotic knows that 2+2=4, but it kills him. A mathematician simply changes the base.

[bishop]

wrong. have you ever taken calculus?

1 times infinity = infinity

every time you include a number, in your example using 2, you're confusing the value of infinity (which has no ultimate value) with a limit.

[ComradeRed]

wrong. have you ever taken calculus? 1 times infinity = infinity every time you include a number, in your example using 2, you're confusing the value of infinity (which has no ultimate value) with a limit.

True, but that is not what I did there. You could theoretically do that, but I am using infinity solely as a variable that is always greater than 0; other than that I do not care at all about it. As long as it is a variable, for that is its sole and only purpose!

[5010]

Originally posted by ComradeRed, but I am using infinity solely as a variable that is always greater than 0

But infinity is a constant. After all... it just keeps going and going... constantly!

[ComradeRed]

But it isn't a constant! It keeps changing! Gets bigger and bigger and bigger and...

[bishop]

True, but that is not what I did there. You could theoretically do that, but I am using infinity solely as a variable that is always greater than 0; other than that I do not care at all about it. As long as it is a variable, for that is its sole and only purpose!

i've never seen the actual term "infinity" used as a variable. i'm not a mathemetician (graduate student in international economics), but usually people use something like X > 0 as the variable. infinity cannot be used as a static variable as far as i'm aware, unless the value is infinity itself.

your first and second examples seem right to me - the first approaches 0 and the second is infinity, but i don't understand your third example. particularly, how does it relate to the other two?

[ComradeRed]

your first and second examples seem right to me - the first approaches 0 and the second is infinity, but i don't understand your third example. particularly, how does it relate to the other two?

*Gasps* I only gave one example! *cue dramatic music*

[bishop]

well... one example in 3 parts.

so, just reword what i said to be "third part", not "third example".

i don't understand what that last bit means, but it seems that was the one you use for your theory.

[ComradeRed]

Well, 1 times infinity = 2 times infinity, thus far, right? divide both sides by infinity, so it becomes 1=2, since the infinities cancel each other out.

[LogicaLunatic]

You can't have your cake and eat it too. If you use infinity you have to use it the same way all through the proof.

To make that proof even close to valid you'd have to include...

2(infinity) = (infinity) + (infinity) (Obvious Rule)
(infinity) + (infinity) = (infinity) (Rule not found anywhere in math, only in theory)

Since there is no mathematical rule for the second one the proof is VALID but not SOUND.

[LogicaLunatic]

Also,

Your rule in number 2 is false.

The multiplication property of equality looks like this...

3 X 6 = 3 X 6

Number 2 kills the proof right there.

LL

[Autolykos]

Originally posted by ComradeRed, Before we begin, allow me to just say I don't mix philosophy and politics togather unlike some phil-itics (like objectivism) so don't hammer away at me in political discussion; afterall, most of the time I just play the devils advocate in philosophical discussion. Lemme begin. A=A, right? Self explanatory. However, could it be possible that A is not A? Absolutely! Take Shrodigner's cat for example! Or math: 1. 1 divided by infinity=2 divided by infinity (GIVEN) 2. 1 (infinity)=2 (infinity) (mulitplication property of equality) 3. 1=2 (division property of equality) Therefore A is not A, if 1=2. Remember: I am just the devil's advocate!

No matter how big the number is, 1 divided by it will be less than 2 divided by it, because 1 > 2. Thus, I guess I disagree with your first proposition: that 1/infinity = 2/infinity.

- Autolykos
"Regentes rectis separati semper sunt."

[Samildanach]

Infinity is NOT a number its a concept more or less meaning ENDLESS.
Every number in itself has the property of an infinity associated with it. For example the number we round to 1 is really 1.0000000 endless string of zeros. Infinities do not have to be variables although they can be eg pi which is infinitely variable as far as we know but they do not have to be.
So really even doing a normal equation such as one plus one is adding two infinities, proving that infinities can be added and subtracted and multiplied and divided.
In classical math anything dived by infinity is approximated to zero. Comrade is quite correct that 1/infinity = 2/infinity. As the difference between them will be impossible to measure. Anything that you can not measure a difference between might as well be the same thing. Autolykos is also theoretically correct because there will be a difference albeit a negligible one.
Thats if you use the mathematical concept of infinity which is an ever increasing positive number.
However consider an infnitiy thats starts at zero and moves in both the x and -x direction. Every increment along the x axis would be cancelled by the -x axis so you would effectively be dividing by 0.
Most of all infinities are about states. If you are going to divide by infinity you have to specify WHICH infinity.

[Samildanach]

Another interesting thing I just thought of is currently to divide by zero is illegal.
I think they have the foundation wrong. For example if you take this back to basics and take an orange and also represent it with the number 10. If we take a knife and look at the orange and decide not to cut it this is the equivalent of dividing by zero. So anything divided by zero should be itself. If we take the knife and cut the orange in half, ie dividing by one ie cutting once the we look at the math and we take 10/1 does not actually equal 10 in reality it equals 2x5.
So if 10/0 = 10 and 10/1 = 2x5

then 10/2 = 3x3.3333 and which reduces to 1=2 as one equals two and there is only one two in the oringinal question then 10/2 reduces to 10/1.
Same with 10/3 = 4x2.5 which reduces to 1=3 and again in the original equation
this means 10/3 becomes 10/1 as there is only one 3 in the original equation.

With this knowledge why is dividing by zero illegal? seems to work perfectly fine to me.

the only thing I really had any problem with whatsoever was the 10/0 = 10
however when you consider that 10/0 means I am going to cut the orange zero times then when you rearrange the equation to form 10 = 10 X 0 then zero means I am going to uncut the orange zero times (ie add bits back together) it seems to work out just fine.