Quite late (Rofl), but this proof is incorrect simply due to the fact that in the second quadrant , the result is negative (meaning ), but you used the positive result.

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- January 2nd 2010, 07:20 AMDefunkt
- January 6th 2010, 09:54 AMrainer
Irrational number - Wikipedia, the free encyclopedia

I saw this the other day. Look under the "History" section. Hippasus' proof that an odd number is even. It's not exactly the same as a 1=2 "proof," but is at the very least relevant to what you are touching upon here.

It's worth mentioning that--if I've understood correctly--a major difference is that Hippasus's proof is valid. No fallacies in logic can be pointed out as in the examples here. I therefore speculate that it is conceivable that a valid 1=2 proof can exist, and that it would merely prove, as Hippasus' proof does, that irrational numbers exist.

My speculation is probably totally hare-brained though, as I am not a real mathematician. - January 7th 2010, 04:06 PMDefunkt
Actually, in his proof he assumes (in contradiction), that there are no irrational numbers. He then reaches a cotradiction - that the number b, which he specified, must be both even and odd, however no such number exists. therefore, the claim that there are no irratioal numbers is false.

- February 8th 2010, 07:13 PMDawson
- October 5th 2011, 12:26 AMmathbyteAnother Proof that 1 = 2
I'm surprised no one brought this one up, since it's been quite a number of years since I first heard of it.

Here is a 1=2 proof using differentiation:

Start with:

x^2 = x^2

x^2 is x*x, so we can represent one side by addition:

x + x + x + ... + x = x^2

where there are x x's.

Now, we differentiate both sides:

1 + 1 + 1 + ... + 1 = 2x

There are x 1's, so we can sum all the 1's to get

x = 2x

And dividing by x we get

1=2 - October 5th 2011, 05:53 AMArchie MeadeRe: Another Proof that 1 = 2
Nice example of what happens if the variable gets partly treated as a constant.

- October 5th 2011, 07:15 PMagentmulderRe: Another Proof that 1 = 2
- October 6th 2011, 03:04 AMArchie MeadeRe: Another Proof that 1 = 2
- October 6th 2011, 04:26 AMagentmulderRe: Another Proof that 1 = 2
- October 7th 2011, 01:08 PMDevenoRe: Another Proof that 1 = 2
let's look at the equation:

when we solve for k, we get k = x.

now, let's differentiate that same equation:

.

when we solve for k, we get k = x/2.

evidently, x = x/2, so 2x = x, so x = 0.

therefore, the flaw in the proof is the very last step...we have divided by 0. - August 16th 2012, 11:25 PMmanoj9585Re: Proof that 1 = 2
-1 = 1

0 = 1 + 1

0 = 2

so it will zero not 1 =2 .

word problem help - August 17th 2012, 07:07 AMWilmerRe: Proof that 1 = 2
Go away with your commercials...

- August 26th 2012, 10:55 AMsmatikRe: Proof that 1 = 2
you made a mistake here bro:

(taking square root)

there should absolute function over cosx. since sqrt(x^2)=abs(x). Its the most common mistake that students makes while learning Pre-calculus.But we soon realize the importance of absolute function when we study limits. - November 27th 2012, 09:39 AMStephen347Re: Proof that 1 = 2
(identity)

(rearranging)

(taking square root)

And thus there is no contradiction when . This absolute value sign must be included if we are taking the positive square root on the right hand side of the equation. - July 20th 2013, 03:59 PMChessTalRe: Another Proof that 1 = 2