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

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 David DeLaney Posts: 65 Registered: 12/12/04
Re: Problems with Infinity?
Posted: Feb 26, 2013 11:52 AM

Frederick Williams <freddywilliams@btinternet.com> wrote:
>Don Kuenz wrote:
>> beginner's language, Cantor uses two sets to define two levels of
>> infinity. One set, Aleph-0, holds countable infinity. The other set,
>> Aleph-1, holds continuum infinity,

>
>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.

Stronger than that - it's provable that it CAN'T settle it one way or another,
unless you extend the theory one way or another (Axiom of Choice, etc., as

>> which includes Aleph-0, along with
>> every possible arrangement of Aleph-0. The infinities of complex
>> variables belong to both sets, as does every other common infinity
>> found in mathematical literature.

>
>Surely not.

Right - "large cardinals" are extremely bigger than either one, and set
theory these days contains a good bit of work on them.

Dave
--
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It's not the clock that slows the hour The definition's plain for anyone to see
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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
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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
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