I know two more of these, but I came across this one today for the first time:
Prove: 1+1=0
Assume: sqrt(-1) = i and that sqrt(a*b) = sqrt(a)*sqrt(b)
Proof:
1 + 1 = 1 + 1
1 + 1 = 1 + sqrt(1)
1+ sqrt(1) = 1 + sqrt[(-1)*(-1)]
1 + sqrt[(-1)*(-1)] = 1 + sqrt(-1)*sqrt(-1)
1 + sqrt(-1)*sqrt(-1) = 1 + (i)*(i)
1 + (i)*(i) = 1 + (i)^2
1 + (i)^2 = 1 + (-1)
1 + (-1) = 1 - 1
1 - 1 = 0
So:
1+1 = 0
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I have not seen that one before either, though I do enjoy that kind of thing.
ReplyDeleteSo did you figure out what's wrong?
ReplyDeleteSorry, that probably came off as insulting.
ReplyDeleteThe problem comes when you assume that sqrt(1)=sqrt[(-1)*(-1)] because that is only one of two solutions, and it is the solution that doesn't actually check out.
ReplyDeleteHey, we got a winner. Congrats. It's like being at FIT all over again!
ReplyDelete