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From: ags@pucc-i (Seaman)
Newsgroups: net.math
Subject: Re: More on i**i
Message-ID: <198@pucc-i>
Date: Tue, 14-Feb-84 11:19:36 EST
Article-I.D.: pucc-i.198
Posted: Tue Feb 14 11:19:36 1984
Date-Received: Fri, 17-Feb-84 03:50:43 EST
References: <229@houem.UUCP>
Organization: Purdue University Computing Center
Lines: 28

The problem with this discussion is that people don't know the difference
between singulars and plurals.  

It makes no sense to say:

  "The value of i**i is well defined.  The values are..."
       ^^^^^				   ^^^^^^

I never said that the VALUES of i**i are not well-defined.

I said the VALUE of i**i is not well-defined.  That statement is correct.

Note that this differs from the situation with other functions that have
universally recognized inverses.  The real square root function is defined
to take the positive branch -- hence sqrt(4) is +2 and not -2.

There is no universally recognized inverse to the complex exponential 
function which is single-valued.  No such inverse can be defined on
the complex plane (excluding the origin) unless you are willing to
put up with a jump discontinuity.

-- 

Dave Seaman
..!pur-ee!pucc-i:ags

"Against people who give vent to their loquacity 
by extraneous bombastic circumlocution."