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[Axiom-mail] Cardinal numbers in Axiom


From: Alasdair McAndrew
Subject: [Axiom-mail] Cardinal numbers in Axiom
Date: Mon, 30 Jun 2008 17:29:38 +1000

Exploring the far reaches of Axiom, I was playing with cardinal numbers:

A:=Aleph(0)
generalizedContinuumHypothesisAssumed true
A^2

returns Aleph(0), as it should.  Now, since A^n=A if n is finite, the command

A^(10^(10^10))

should return Aleph(0).  But it doesn't - it just hangs Axiom.  It seems as though Axiom is first trying to evaluate 10^(10^10), and then raise A to that power.  But surely Axiom should recognize that 10^(10^10) is finite immediately, and proceed from there.

-Alasdair

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