let a = b -> a^2 = b^2 = ab -> a^2 - b^2 = a^2 - ab -> (a+b)(a-b) = a(a-b) divide by (a-b)... -> a+b = a as b=a.. -> a+a = a -> 2a = a divide by a.. -> 2 = 1 -> 1 = 0 (-1) -> a = 0 (*a) This proves that 1=2, 0=1, and in general, any number is equal to 0. ...im confused ~Callum

In mathematics you can't divide anything by zero In the above you said That can't be done as a=b you can't divide by (a-b) as it is dividing by zero. that is mistake in the whole process.

This is the puzzle in the first few pages on "mathematical games and puzzles" by Rajesh kumar Thakur. I've already seen this absurd problem.

then in that step the equation becomes infinity = infinity then where the remaining steps comes from.....

-1/1 = 1/-1 taking square root on both sides (-1/1)^1/2 = (1/-1)^1/2 now as i^2 = -1 i/1 = 1/i now dividing by 2 on both sides i/2 = 1/2i adding 3/2i on both sides and now multiplying by i on both sides i^2/2 +3/2 = 1/2 + 3/2 -1/2 + 3/2 = 4/2 1= 2 ---------- Post added at 07:07 PM ---------- Previous post was at 07:06 PM ---------- gsonline going to find fault in this. ---------- Post added at 07:16 PM ---------- Previous post was at 07:07 PM ---------- I would like to correct gsonline. "in mathematics we cannot divide by zero". Its infinity as said by alex. Actually we don't have discovered what 0/0 is yet. (a+b)(a-b)/(a-b) = (a+b)0/0 = 0/0 did you get the mistake.