Date: Feb 26, 2013 5:47 PM
Author: Wayne Throop
Subject: Re: Problems with Infinity?
: "Brian M. Scott" <b.scott@csuohio.edu>

: 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.

Wait... this is also true for one dimension?

How do you get more than one path on a line?

Um... hm, vary destination I expect. Nevermind.

So... the guy who was correcting Gamow on the page

http://www.ii.com/math/ch/confusion/

was also incorrect? Specifically

Also note that he is assuming [...] GCH

when he says "there are aleph2 different curves".

That is, the GCH does *not* imply there are aleph2 different curves,

and the feller should have added "and he was wrong about that,

because requiring continuity (of the paths?) eliminates most of them"?

Related to the "restriction to D" in

http://math.stackexchange.com/questions/89103/cardinality-of-set-of-simple-closed-curves

which is what knocks it back from 2^omega from 2^(2^omega),

if I'm reading rightly.

Thanks for persisting in making it clear(er I hope) to me.