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How do I define a range of a symbol?

• To: mathgroup at christensen.cybernetics.net
• Subject: [mg876] How do I define a range of a symbol?
• From: hsvrt@uunet
• Date: Thu, 27 Apr 1995 01:48:40 -0400
• Organization: University of Bergen, Norway

Can anyone help me with the following (probably elementary) problem:

Is it possible to specify a range of a constant, e.g.

0 < k < Infinity, or
0 < k < 100, or
k not equal to 0

in a Mathematica session? I use Mathematica to do some heavy symbolic 
computation, and problems occur because Mathematica doesn't dare to do 
simplifications in which you have to assume that k is positive, not-zero etc.

Is there also a way to give Mathematica qualitative information about 
functions in order to improve calculation of limits etc? For instance, if

f: R->R

increases on R, then lim f(x) / Exp[f[x]] = 0 as x approaches (+) Infinity. 
But how do I instruct Mathematica to understand this?

Please help me,

Roger Strand
Dept of Biochemistry and Molecular Biology
University of Bergen, Norway
e-mail roger.strand at svt.uib.no