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Agenradbo.134 net.math utzoo!decvax!genradbo!al Thu May 6 13:59:21 1982 oldie but goodie (sqrt)

The problem with the sqrt problem has nothing to do with dividing by zero or because complex numbers are being used. As some others have stated, the problem is totally because sqrt(x) is a multi-valued function. We know that sqrt(1) is both 1 and -1. One could as well prove in the real number domain:

sqrt(1) = sqrt(1/1) = sqrt(1)/sqrt(1) = (-1)/1 or 1 = -1

Stated this way, of course, the problem is obvious. Paradoxical proofs must obscure what is really happening to seem paradoxical. For the original proof given, remember that sqrt(-1) is both i and -i.

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