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Can anyone prove "1=2" ? if so HOW ???

Note by Dilip Kumar
5 years ago

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It is impossible. This can be "proven" with a fallacious "proof". You could also make your own "mathematics" wherein "1=2" holds. However, that "mathematics" would be inconsistent with the conventional mathematics.

An example of a kind of mathematics where $$1 = 2$$ holds, would be looking at the fractional part of a real number (sometimes also known as working modulo 1).

Recall that $$\lfloor x \rfloor$$ is the greatest integer function, which gives you the integer part of a number. The fractional part of a (positive) real number is given by $$\{ x \} = x - \lfloor x - \rfloor$$. You should be able to verify that the basic arithmetic operations still hold, and is consistent in the equivalence class.

This was popular in the past especially when logarithms were used to multiply large numbers, and looking at the fractional part of the logarithm gives you the initial starting digits. With the invention of calculators, it has fallen out of use and is now mainly used by computers to determine rounding.

Staff - 5 years ago

It is provable..but the reason why the proof breaks down is very obvious, basic and this proof is foolish :P The proof goes like this. we know that $$(a^2 -b^2)$$= $$(a + b)(a - b)$$ let us consider $$a = b$$ we have $$(a^2 - a^2)$$ = $$(a + a)(a - a)$$ [This is where everything gets foolish]now, $$a(a - a)$$ = $$(a + a)(a - a)$$ [Ridiculous] cancelling $$(a - a)$$ on both sides, we are left with $$a$$ = $$a + a$$ or $$a = 2a$$ now cancelling $$a$$ on both sides, 1 = 2 :P

- 5 years ago

The reason that this fails is because we can't divide by $$a - a = 0$$.

- 5 years ago

yeah..

- 5 years ago

We can "Proof that 0 = 1" ( :) ) then add $$1$$ for both sides to obtain $$1 = 2$$.

- 5 years ago

Dude, stop trying to spew fraudulent material. It's not even a proper proof.

- 5 years ago

Chill out everybody. I'm pretty sure he was just making a joke. Hence the emoticon in the parentheses.

Staff - 5 years ago

No dude, read that proof properly. it says it is incorrect. you're asked to find out where the mistake is...

- 5 years ago

I know.

- 5 years ago

then

It is impossible to prove that $$1 = 2$$ with a correct proof.

- 5 years ago

no, it can be proved correctly, read the first comment. It sums up the situation pretty nicely.

- 5 years ago

Zi Song,the method used to obtain that proof wouldn't work for 1 and 2

- 5 years ago