Date: Feb 24, 2013 11:04 PM
Author: David DeLaney
Subject: Re: Problems with Infinity?

garabik-news-2005-05@kassiopeia.juls.savba.sk wrote:
>William Elliot <marsh@panix.com> wrote:
>> Cantor did not deal with geometric infinity.
>> His infinities are the cardinalities of sets.

>
>Or with infinite ordinals, which is not quite the same sort of infinity.
>Are there any (good) SFnal stories concerning cardinal(ities),
>transfinite induction, supertasks, actual infinities and other esoteric
>phenomena?
>
>I am aware of White Light by Rudy Rucker, The Infinite Assassin by Greg
>Egan and Luminous by the same author. However, they barely touch the
>cardinality of c.


There's also the series of Wheelie Willie comix in Rucker's _Infinity and the
Mind_, and infinities make sporadic appearances here and there in his other
works, but White Light is his Infinity Novel, yep.

Taking a quick look at the collection _Mathenauts_, which happens to be within
reach of my left hand without even moving, only Niven's _Convergent Series_
reminds me just from the title that it also deals with the subject. ...
Checking, that's about it from there.

>As Kronecker put it, "God made natural numbers; all else is the work of
>man", therefore denying the existence of higher cardinals (or even
>finitism) is a valid philosophical approach - after all, you can get
>many interesting results by negating the axiom of infinity...


Oh yes. "Only finite numbers and fractions exist" is consistent. But it gets
into conflicts with, like, 2D geometry, because there's no pi, and no square
root of 2...

Dave
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