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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