: "Brian M. Scott" <firstname.lastname@example.org> : 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.
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"?