A is not A

[5010]

10/1= how many ones are in a ten = 10, 10(1)=10

10/2= how many twos are in a ten = 5, 5(2)=10

10/0= how many zeros are in a ten? There is no such answer. No matter how many zeros you have it will never amount to anything more than zero.

[ComradeRed]

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

No, the property that states that if you multiply both sides of an equation by the same number, the sides remain equal.

I multiply both sides by infinity. Which would actually cancel out right there, to become 1=2

[Autolykos]

Originally posted by 5010, 10/1= how many ones are in a ten = 10, 10(1)=10 10/2= how many twos are in a ten = 5, 5(2)=10 10/0= how many zeros are in a ten? There is no such answer. No matter how many zeros you have it will never amount to anything more than zero.

And I think you just explained why it took so long for human beings to use "zero" as a mathematical concept, and why it took so long for place-holding numerals to be used.

- Autolykos
"Regentes rectis separati semper sunt."

[ericsp23]

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!

The flaw in your reasoning is the assumption that infinity=infinity. It is simple to demonstrate that that is not a valid assumption to make. Take, for example, the set of all rational numbers that are greater than 0 and less than 1. This set has an infinite number of elements. Now consider the set of rational numbers that are greater than 0 and less than 2. Again, there are an infinite number of elements, but common sense tells us that the set of numbers between 0 and 2 is twice as large as the set of numbers between 0 and 1. You can also compare the set of all positive integers and all positive integers that are even. Both sets are infinite but common sense tells us that one is half as big as the other.

So with this in mind, 1 divided by infinity is NOT equal to 2 divided by infinity. 1 divided by infinity is what I would call an "infintessimal" (an infinitely small amount) and 2 divided by infinity would be an infintessimal twice as big. Also, 1(infinity) does NOT equal 2(infinity). The second would be twice as large as the first. So, therefor your conclusion that 1=2 does not stand.

Edited for spelling.

[bishop]

heh.. seems like everyone has their own answer here.

[5010]

Originally posted by bishop, heh.. seems like everyone has their own answer here.

Maybe there are an infinite number of true answers, and an infinite number of false answers.

[CmJour]

ComradeRed:

A=A, right? Self explanatory. However, could it be possible that A is not A? Absolutely!

Then what your saying is not what your saying.





LogicalLunatic:

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.

But then he would only be consistent to "prove" that he never had to be.

[ComradeRed]

Suppose A were the thesis, couldn't A be both the thesis AND anti-thesis? Like in quantum mechanics, but it is perceived to be only the thesis.

[CmJour]

Quantum Mechanics has various interpretations to it, I am biased towards not interpeting it as entailing that contradictions can exist in reality because we can't think in contradictions. If you except contradictions in one aspect of reality, it is arbitrary to limit contradictory thinking to that one area because there would be no reason not think in contradictions all of the time. But if that happened, it would be the end of science and rationality. But then quantum mechanics would be a science to end science.

[bugsbunny04]

Originally posted by 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)

I dont think you can multiply/divide by infinity. Or add/subtract to it for that matter. Infinity is more of a concept than a number. You can never say it is x because infinity means you can have x+x so it cant be x.

It is neither an undefined variable, nor number, because it lacks function of either.

[samsara15]

A statement can be true or false or indeterminable. For example, the statement: I always lie.

[GreatWyrm of Babylon]

Being an engineering major, I am the next best thing to a mathematics major.

You cannot place a counting number and a conceptual concept together in an equation without qualifing your exceptions. Like was mentioned by another poster, 1 and 2 do not actually exist anywhere in the universe. Therefore any equation using those numbers is a transform equation and has to have qualifiers. In electronics we use LaPlace and Z-transforms, but they have rules about when they can be used and when they cannot. Fact is, many 'pure' mathematics people refuse to even use them then, but doing the math without them uses a lot of paper.

Infinity is often used in pre-calc to explain limits, but even there if you do not follow the rules properly you end up with a mess of contradictions.

BTW: If 2+2 is used to represent real physical numbers with a single significant figure... 2+2=5 for large enough values of 2, since 2 represents a number between 1.5 and 2.5. (2.49+2.49=4.98 rounding the numbers before adding gives a different answer than rounding after adding.)

If you really want to fiddle with a puzzle.
1) 1=1
2) divide both sides by 3, leaving one a fraction the other a decimal.
3) multiply both sides by 3 getting 1=0.999999999999999(repeating)

[ImAlwaysRight]

The fallacy in this riddle lies with the first assertion that:

1/infinity = 2/infinity

This if false because any number divided by infinity is not a number at all - it is "undefined". The equation only holds true in the sense that both numbers are "undefined". The "words" babbilak and scrumpletoast are undefined words and are, therefore, not really words at all. But even if you insisted on saying they are words, they are obviously not equal.

By way of proof:

1. If 1/infinity = 2/infinity was true, then multiplying both sides by infinity would yield another true equation.

2. But when we perform that operation,

(1/infinity)*infinity = (2/infinity)*infinity

3. We are left with

1=2 , which is false.

4. Therefore, the first assertion that

1/infinity = 2/infinity

is false and invalidates the rest of the riddle.

[ComradeRed]

The "words" babbilak and scrumpletoast are undefined words and are, therefore, not really words at all.

Not true, all a word has to do is convey meaning. Definition is the attempt to articulate meaning, but is not the same.

[ImAlwaysRight]

OK, Let me be more to the point. 1/x never equals 2/x whatever quantity x represents. Why should we think that it would be any different when x=infinity? But as it turns out, in that special case, (1/infinity) and (2/infinity) are both undefined "quantities" and therefore are not quantities at all. So to assert that they are quantitatively equal is wrong no matter how you look at it. It is setting up this error early in the equation that allows you to manipulate it to arrive at the absurd conclusion that 1=2.

[Zeebadee]

"1. 1 divided by infinity=2 divided by infinity (GIVEN)"

Just because you claim it's a "given" doesn't make it so.

[unicx]

Ok everyone has overcomplicated this.... as ...well it is philosophy... as i could do the same... but i am going to keep it simple and go ahead and call me a moron for doing so... In "reality" 1 cannot equal 2... (if you are looking at a table with oranges on it and you grab two and your friend grabs one you do not have the same number of oranges as your friend does) and in reality A is always A. I find that most philosophical debates are just flaws in language. Because in most philosophical debates you can describe the answer but cannot come up with a word for it. I am not saying that applies to this particular debate but if you think about it, it does apply to many. I'm not sure who is actually going to grasp what i just stated in this rant, not because anyone here is stupid, but because i don't want to go on and on at the moment to accuratly describe it.

[Zeebadee]

This is a particularly weak fallacy. For much better false proofs check out:

http://mathforum.org/dr.math/faq/faq.false.proof.html