From: utzoo!utcsrgv!roderick
Newsgroups: net.math
Title: Re: Solution(?) to oldie but goodie
Article-I.D.: utcsrgv.1099
Posted: Thu Feb 24 11:28:22 1983
Received: Thu Feb 24 11:46:23 1983
References: pyuxjj.176

The problem is that the definition of  i  is not  i = sqrt(-1),
but that  i**2 = -1.  These are two completely different things,
despite the tempting intuitiveness of the former.  Any experience
with abstract algebra (especially extension fields; C is R extended
with a symbol  i  defined by  i**2 = -1) and you will understand
why things like this are done.  (For one thing, they don't lead
to contradictions like the one you gave.)  Finally note that
square root is defined as a value which squared gives the original
number; in the strictest sense, it is not even a function.

Rod Glover
U of T
..!utzoo!utcsrgv!roderick