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Apsuvax.1046 net.math utzoo!decvax!harpo!eagle!mhtsa!allegra!psuvax!sibley Thu May 6 13:32:19 1982 Re: Oldie but goodie There seems to be some confusion over the 'oldie but goodie' paradox which appeared here the other day. The difficulty is that square root is NOT a function when defined on all real numbers. The usual convention is to define it only for non- negative real arguments and to define the value to be the non-negative square root of the argument. But every real number (indeed, every complex number) except 0 has two different square roots. Which one do you pick for the value of the square root function? Well, the argument in the 'oldie but goodie' (or other similar ones) just shows that there is no way to assign values which will allow the 'usual' rules of arithmetic when extending the domain to include more than the non-negative reals.

dave psuvax!sibley

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