Mathmatical proof that 2 = 1? Well, clearly 2 does not equal 1, so what's the deal with the math below?
See if you can figure out why 2, indeed, does not equal 1. There's something fishy about the math below... Don't cheat and Google the answer until you've at least tried to work it out (*cough*SARAH*cough*)...
Leave a comment and I'll update this in a few days.
a = b
a^2 = a*b
a^2-b^2 = a*b-b^2
(a+b)(a-b) = b(a-b)
(a+b) = b
a+a = a
2a = a
2 = 1
a^2 = a*b
a^2-b^2 = a*b-b^2
(a+b)(a-b) = b(a-b)
(a+b) = b
a+a = a
2a = a
2 = 1
HINT: Work though this as they teach you in school - show ALL your work.
So I never did this before but I was just looking at it - and no, I didn't Google anything... But wouldn't (a+b)(a-b)=b(a-b) be (a-b)(0)=b(0) which means 0=0?
ReplyDeleteBut doesn't 0=0? What's wrong with that? You're very close to the error in the math though... it is that step and the next...
Delete0 does =0 but then there wouldn't be another step. The problem is over based on order of operations.
ReplyDelete(a+b)(a-b) = b(a-b)
(a+b)(0) = b(0)
0 = 0
What am I missing? This debunks the 2=1 because these steps are not correct.
Yet, you don't seem to have a problem with the step above "a^2-b^2 = a*b-b^2". Interesting... 0=0 is true and doesn't mean the "proof" is over...
Delete