MathGroup Archive 2001

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Truth in inequalities

  • To: mathgroup at
  • Subject: [mg29347] Truth in inequalities
  • From: Jack Goldberg <jackgold at>
  • Date: Thu, 14 Jun 2001 02:27:25 -0400 (EDT)
  • Sender: owner-wri-mathgroup at

Hi group,

Can someone explain the logic of the following:

	x < Infinity 	  	returns 	x < Infinity
	x - Infinity < 0  	returns  	True

I should mention that I am aware of the fact that x - Infinity simplifies
automatically to -Infinity which is then compared to 0 and found wanting.
The issue I'm raising is why should a CAS that has  x-Infinity < 0 return
True not also return True for the  x < Infinity?  One awkwardness of
having this difference of behavior can be seen in the example,

MyFunction[x_,y_]/;(x<y) :=  blah


MyFunction[x_,y_]/;(x-y<0)  := blah

do not do the same thing when, say, y=Infinity. 

Just curious :-)


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