Re: Aleph question
- From: magidin@xxxxxxxxxxxxxxxxx (Arturo Magidin)
- Date: Tue, 9 May 2006 01:01:59 +0000 (UTC)
In article <1147123641.709454.131050@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Guy L. <gihyunlee@xxxxxxxxx> wrote:
Please learn to quote.
http://groups.google.com/support/bin/answer.py?answer=14213&topic=250
Would this solution also work:
No since, cofinality of 2^aleph_0 is uncountable by Konig's Thm but
cofinality of aleph_(w1*5+w) = aleph_(w1*5+w),
Do you know what "cofinality" means? The cofinality of aleph_{w1*5+w}
is not aleph_{w1*5+w}, it is in fact omega: the subset
{aleph_{w1*5+i} | i in omega} is cofinal in aleph_{w1*5+w}, and since
infinite cardinals are all limit ordinals, it cannot be any smaller
than omega.
therefore 2^aleph_0 cannot equal aleph_(w1*5+w)
Yes. 2^{aleph_0} cannot be a cardinal with cofinality omega. There are
other conditions that restrict possible values of 2^{aleph_0}, as I
recall (though I could be wrong), but this is the easiest one.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes")
======================================================================
Arturo Magidin
magidin@xxxxxxxxxxxxxxxxx
.
- Follow-Ups:
- Re: Aleph question
- From: matthias
- Re: Aleph question
- From: Guy L.
- Re: Aleph question
- From: Guy L.
- Re: Aleph question
- From: Guy L.
- Re: Aleph question
- References:
- Aleph question
- From: Guy L.
- Re: Aleph question
- From: Arturo Magidin
- Re: Aleph question
- From: Guy L.
- Aleph question
- Prev by Date: Re: a book to give the "geography" of "the land of mathematics"
- Next by Date: Re: seek a map of the geography of the land of mathematics
- Previous by thread: Re: Aleph question
- Next by thread: Re: Aleph question
- Index(es):
Relevant Pages
|
