Re: [Axiom-mail] Cardinal numbers in Axiom

[Themos Tsikas]

Hello 

All Axiom knowledge is organised into types, not operations.  In your case, I 
cannot imagine a practical situation where the expression A^(10^(10^10)) 
would turn up. But I suppose one can rewrite Integer so that some 
calculations are lazy. One would then pay the runtime price for a complicated 
representation for each and every Integer operation. There doesn't seem to be 
enough of an upside to warrant this but there may be one in the future.

Regards
Themos Tsikas



On Monday 30 June 2008, Alasdair McAndrew wrote:
> 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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