Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

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


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: The finite infinite and the infinite infinite
Replies: 48   Last Post: Sep 4, 2012 4:00 PM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
David Hartley

Posts: 411
Registered: 12/13/04
Re: The finite infinite and the infinite infinite
Posted: Aug 24, 2012 6:40 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In message
<cc4504cf-e8b4-4a94-a1a0-d9c1785ce5f5@c4g2000yqi.googlegroups.com>,
MoeBlee <modemobe@gmail.com> writes
>On Aug 24, 3:02 pm, WM <mueck...@rz.fh-augsburg.de> wrote:
>> If there were sets that
>> could not be well-ordered, then they had no ordinal number. And then
>> their cadinal number could not be fixed.

>
>That is, if we use a certain definition of "card", yes.


There is no associated aleph, yes, but the set still has cardinality and
a cardinal can be defined using "Scott's trick".

>> There would exist sets A and
>> B for which the cardinalities were not in trichotomy.

>
>More exactly, it would be the case that we can't prove that for every
>set A and B, either card(A) =< B or card(B) <= card(A).
>
>It would NOT be the case that we could provide examples of sets A and B
>that don't satisfy card.
>
>Most importantly, it would NOT be the case that we could prove:
>
>There exist sets A and B such that A and B fail trichotomy.


Are you sure? If A cannot be well-ordered but B can, then
card(B)<= card(A) is possible, but card(A) <= card(B) is not.
However, you can not have card(B) <= card (A) for every well-orderable
B, so there will be some B which is incomparable with A. In particular
there will be a least aleph incomparable to A. It is called the Hartog's
number of A. http://en.wikipedia.org/wiki/Hartogs_number
--
David Hartley


Date Subject Author
8/23/12
Read Re: The finite infinite and the infinite infinite
Jesse F. Hughes
8/24/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/24/12
Read Re: The finite infinite and the infinite infinite
Frederick Williams
8/24/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/24/12
Read Re: The finite infinite and the infinite infinite
Virgil
8/24/12
Read Re: The finite infinite and the infinite infinite
MoeBlee
8/24/12
Read Re: The finite infinite and the infinite infinite
David Hartley
8/24/12
Read Re: The finite infinite and the infinite infinite
MoeBlee
8/24/12
Read Re: The finite infinite and the infinite infinite
Virgil
8/25/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/25/12
Read Re: The finite infinite and the infinite infinite
Virgil
8/26/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/26/12
Read Re: The finite infinite and the infinite infinite
Virgil
8/27/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/27/12
Read Re: The finite infinite and the infinite infinite
MoeBlee
8/27/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/27/12
Read Re: The finite infinite and the infinite infinite
MoeBlee
8/28/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/28/12
Read Re: The finite infinite and the infinite infinite
Virgil
8/28/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/29/12
Read Re: The finite infinite and the infinite infinite
Virgil
8/29/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/29/12
Read Re: The finite infinite and the infinite infinite
Virgil
8/27/12
Read Re: The finite infinite and the infinite infinite
Virgil
8/24/12
Read Re: The finite infinite and the infinite infinite
MoeBlee
8/24/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/24/12
Read Re: The finite infinite and the infinite infinite
MoeBlee
8/24/12
Read Re: The finite infinite and the infinite infinite
Virgil
8/24/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/24/12
Read Re: The finite infinite and the infinite infinite
MoeBlee
8/24/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/24/12
Read Re: The finite infinite and the infinite infinite
MoeBlee
8/24/12
Read Re: The finite infinite and the infinite infinite
Virgil
8/24/12
Read Re: The finite infinite and the infinite infinite
Virgil
8/25/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/25/12
Read Re: The finite infinite and the infinite infinite
Virgil
8/31/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
8/31/12
Read Re: The finite infinite and the infinite infinite
Virgil
9/2/12
Read Re: The finite infinite and the infinite infinite
mueckenh@rz.fh-augsburg.de
9/2/12
Read Re: The finite infinite and the infinite infinite
Virgil
9/3/12
Read Who is better, Virgil or Russell?
mueckenh@rz.fh-augsburg.de
9/3/12
Read Re: Who is better, Virgil or Russell?
FredJeffries@gmail.com
9/3/12
Read Re: Who is better, Virgil or Russell?
Virgil
9/3/12
Read Re: Who is better, Virgil or Russell?
Virgil
9/3/12
Read Re: Who is better, Virgil or Russell?
mueckenh@rz.fh-augsburg.de
9/3/12
Read Re: Who is better, Virgil or Russell?
Virgil
9/4/12
Read Re: Who is better, Virgil or Russell?
mueckenh@rz.fh-augsburg.de
9/4/12
Read Re: Who is better, Virgil or WM?
Virgil

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.