
Re: Problems with Infinity?
Posted:
Feb 26, 2013 5:34 PM


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

