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

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Butch Malahide

Posts: 894
Registered: 6/29/05
Re: Problems with Infinity?
Posted: Apr 11, 2013 11:18 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Apr 11, 7:52 pm, "Brian M. Scott" <b.sc...@csuohio.edu> wrote:
> On Thu, 11 Apr 2013 20:40:31 -0400, Walter Bushell
> <pr...@panix.com> wrote in
> <news:proto-E08F93.20403111042013@news.panix.com> in
> rec.arts.sf.written,sci.math:
>

> > In article <512CA332.AD4F7...@btinternet.com>,
> >  Frederick Williams <freddywilli...@btinternet.com> wrote:

> >> That the cardinality of the continuum (c = 2^{aleph_0})
> >> is equal to aleph_1 is Cantor's continuum hypothesis
> >> which modern set theory settles neither one way nor the
> >> other.

> > Does anyone care.
>
> Yes.
>

> > That is do any important results hang on either one?
>
> There are results in a variety of fields, from commutative
> algebra through functional analysis and topology to complex
> analysis, that depend on CH.  Some of them involve questions
> of a fairly fundamental character.


In complex analysis, Paul Erdos showed that the continuum hypothesis
is *equivalent* to the existence of an uncountable family F of entire
functions such that {f(z): f in F} is countable for each complex
number z.

http://www.renyi.hu/~p_erdos/1964-04.pdf


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

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