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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 4:44 PM

:: 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. I see (or google) that
I most likely original got that meme from Gamow's "One Two Three...
Infinity". Here, some of what he says is corrected:

http://www.ii.com/math/ch/confusion/
An example of confusion is in George Gamow's One Two Three...Infinity.
On page 34 he says:
The sequence of numbers (including the infinite ones!) now runs:
1 2 3 4 5 ... aleph1 aleph2 aleph3 ...
and we say "there are aleph1 points on a line" or "there are aleph2
different curves" ...
First note that Gamow's sequence of finite and transfinite numbers is
not correct. It should be:
1 2 3 4 5 ... aleph0 aleph1 aleph2 aleph3 ...
Also note that he is assuming CH when he says "there are aleph1 points
on a line" and GCH when he says "there are aleph2 different
curves."

However, these confusions and others don't seem to invalidate the notion
I had about "bigger still", since per above, the GCH seems to imply it.
Or am I still missing something? Probably conflating omega with something.

Granted, even if I'm not missing and didn't conflate, it would imply
I inadvertently drug the GCH in without notice, so

"Insofar as I may be heard by anything, which may or may not care
what I say, I ask, if it matters, that I be forgiven for anything
I may have done or failed to do which requires forgiveness."
--- paraphrased excerpt from the Possibly Proper Death Litany,
from Creatures of Light and Darkness

"Lord, I apologize fer that."
--- Larry the Cable Guy's condensed version

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