alt Hacker NewsDoesn't this allow one to prove x=y for any x, y?
x/0 = x(1/0) = x*0 = 0, so x/0 = 0 for all x.
So x/0 = y/0.
Multiply both sides by 0: x = y.
Replies
rnhmjoj • today at 2:32 PM
No, because x/y is just an arbitrary operation between x and y. Here you're assuming that 1/x is the inverse of x under *, but it's not.
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What theorem did you use that allowed you to multiply both sides by $0$? (That theorem had conditions on it which you didn't satisfy.)