Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Problems with Infinity?
Replies: 72   Last Post: Apr 12, 2013 1:36 PM

 Messages: [ Previous | Next ]
 Wayne Throop Posts: 127 Registered: 12/12/04
Re: Problems with Infinity?
Posted: Feb 26, 2013 5:47 PM

: "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),

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

Date Subject Author
2/24/13 William Elliot
2/24/13 garabik-news-2005-05@kassiopeia.juls.savba.sk
2/24/13 Frederick Williams
2/24/13 David DeLaney
2/25/13 P. Taine
2/26/13 Butch Malahide
2/24/13 jsavard@ecn.ab.ca
2/25/13 ross.finlayson@gmail.com
2/25/13 Brian M. Scott
2/25/13 Shmuel (Seymour J.) Metz
2/25/13 jsavard@ecn.ab.ca
2/25/13 Brian M. Scott
2/26/13 ross.finlayson@gmail.com
2/26/13 Frederick Williams
2/26/13 Wayne Throop
2/26/13 Brian M. Scott
2/26/13 ross.finlayson@gmail.com
2/25/13 Frederick Williams
2/25/13 Shmuel (Seymour J.) Metz
2/25/13 Frederick Williams
2/26/13 Wayne Throop
2/26/13 Wayne Throop
2/26/13 Brian M. Scott
2/26/13 Wayne Throop
2/26/13 Brian M. Scott
2/26/13 Wayne Throop
2/27/13 David DeLaney
2/27/13 Shmuel (Seymour J.) Metz
2/28/13 David DeLaney
2/28/13 Shmuel (Seymour J.) Metz
2/28/13 David DeLaney
3/1/13 Shmuel (Seymour J.) Metz
3/1/13 David DeLaney
3/2/13 Shmuel (Seymour J.) Metz
2/28/13 jsavard@ecn.ab.ca
2/28/13 David Johnston
2/27/13 Shmuel (Seymour J.) Metz
2/26/13 Frederick Williams
2/26/13 David DeLaney
4/11/13 Walter Bushell
4/11/13 Brian M. Scott
4/11/13 Butch Malahide
4/12/13 fom
4/12/13 Wayne Throop
4/12/13 fom
4/12/13 Wayne Throop
4/12/13 fom
4/11/13 jsavard@ecn.ab.ca
4/11/13 Butch Malahide
4/12/13 Virgil
4/12/13 Brian M. Scott
4/12/13 jsavard@ecn.ab.ca
4/11/13 fom
4/11/13 Butch Malahide
4/11/13 Butch Malahide
4/12/13 Brian M. Scott
4/12/13 Butch Malahide
2/26/13 Brian M. Scott
2/26/13 Shmuel (Seymour J.) Metz
2/26/13 Brian M. Scott
2/26/13 David Bernier
2/26/13 Shmuel (Seymour J.) Metz
2/28/13 Shmuel (Seymour J.) Metz
4/11/13 Walter Bushell
4/11/13 Shmuel (Seymour J.) Metz
2/26/13 Frederick Williams
2/27/13 Scott Fluhrer