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Re: Problems with Infinity?
Posted:
Feb 26, 2013 5:34 PM
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On Tue, 26 Feb 2013 21:44:09 GMT, Wayne Throop
<throopw@sheol.org> wrote in <news:1361915049@sheol.org> in
rec.arts.sf.written,sci.math:
>:: Similarly, the cardinality of the set of paths in n>=2 d space
>:: (if I'm remembering a close enough description) is bigger still.
>: "Brian M. Scott" <b.scott@csuohio.edu>
>: No, it's also 2^\omega, since by definition a path is continuous.
> Do you mean points on the... ah, no wait.
No, I mean the number of paths. And the dimension is
irrelevant here so long as it is finite and positive.
For finite n,m > 0 there are 2^c functions from R^n to
R^m, which is more than c and is what Gamow had in mind,
but requiring continuity eliminates most of them, leaving
only c paths.
[...]
Brian
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