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spidermonky

Math Problem

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Can anyone explain why this works??



I sucked in basic number theory, but I think the logical fallacy is in step 5: "0 / 0 = 0 / 0" is not true in the way they mean it to be, because 0 / 0 is actually undefined (or the infinite set; see below), not a number.

The meaning of the value "x / 0" is any number that, multiplied by the denominator, equals the numerator. When the numerator is non-zero, we say the value of "x / 0" is undefined because no number multiplied by zero equals the numerator. And when the numerator is zero, as in this math problem, the value "x / 0" (or "0 / 0") is undefined because ALL numbers multiplied by zero equal the numerator.

So step 5 is some sort of infinite set relationship, and that doesn't help prove the rest of the problem.

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Pull.

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Division by zero is illegal. This is some dude's fallacy, I think, just presented a different way than I'm used to seeing it. I forget the exact name of the fellow. You can probably find it at http://mathworld.wolfram.com if you're really interested. The site's search engine is pretty good.

You can start it by saying x^2-x^2=x^2-x^2 and take pretty much the same route as well.

Blues,

Vinny
Vinny the Anvil
Post Traumatic Didn't Make The Lakers Syndrome is REAL
JACKASS POWER!!!!!!

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that was extra credit on one of my tests once. you can't divide by zero




Sure ya can. Its just that the answer is always infinity B|



If I may refer you to my plush response above, infinity times zero is not non-zero, so any non-zero number divided by zero is not infinity, it's "no number exists". And all numbers time zero are zero, so infinity times zero is not the only number that 0 divided by 0 "equals".

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That's pretty funny dude. Hehehehe. It's ok if you pronounce it 'zaaaay-ro' or 'naught' but if you pronounce it like a Yankee or 'fuhriner' it's considered a capital offense.

A&M produces some damned fine engineers though.
Vinny the Anvil
Post Traumatic Didn't Make The Lakers Syndrome is REAL
JACKASS POWER!!!!!!

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A&M produces some damned fine engineers though.



Of course, you have to play on the track at their house. ;)

The basic issue with the problem is the introduction of extraneous roots by raising the power of the equation. By going from X^1 to X^2, you introduce possible roots. All the other problems sort themselves out if you don't do that.

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Infinity is not a number. a/x as x->0 is infinity in the sense that it gets arbitrarily large, but it is not equal to infinity, or anything else for that matter, because the limit does not exist. Far too many a calc student has gotten confused by this notation.

a/0 is a number b such that 0*b=a. Unless a is zero, clearly no such number exists. If a is zero b can be anything, so 0/0 is usually undefined because it has multiple values and we would like to consider multiplication as a function in algebra.

-- Toggle Whippin' Yahoo
Skydiving is easy. All you have to do is relax while plummetting at 120 mph from 10,000' with nothing but some nylon and webbing to save you.

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I have another good one:



______
2 / 2 | ____ 2 2
1 = (-1) = \/ (-1) = \/(-1)| = i = -1

Therefore, 1 = -1.


-- Toggle Whippin' Yahoo
Skydiving is easy. All you have to do is relax while plummetting at 120 mph from 10,000' with nothing but some nylon and webbing to save you.

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As well as a whole bunch of other identities, yeah;)

Most people see that as a proof of 1=-1. In reality, it's a disproof of an identity of square roots over the complex numbers.

-- Toggle Whippin' Yahoo
Skydiving is easy. All you have to do is relax while plummetting at 120 mph from 10,000' with nothing but some nylon and webbing to save you.

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