Fwd: Cardinality of the MW

From: <GSLevy.domain.name.hidden>
Date: Wed, 14 Jul 1999 00:38:44 EDT

>
> Note that there is some dispute in the mathematical world over how big
> c is. Some suggest that it is a rather small infinite cardinal, possibly
> aleph-one, meaning the second smallest one (just above aleph-zero,
> which is the cardinality of the integers). Others suggest that it may
> be larger, possibly much larger, bigger than aleph-(aleph-zero).
>
> Hal

For philosophical reasons it would be nice for the MW to be of cardinality
omega, larger than all of Cantor's infinities. If the MW is also a continuum,
then the continuum may be of size omega. Does it make any sense?

George

attached mail follows:



>
> Note that there is some dispute in the mathematical world over how big
> c is. Some suggest that it is a rather small infinite cardinal, possibly
> aleph-one, meaning the second smallest one (just above aleph-zero,
> which is the cardinality of the integers). Others suggest that it may
> be larger, possibly much larger, bigger than aleph-(aleph-zero).
>
> Hal
>
>

My memory is fading somewhat about transfinite cardinal
numbers. However, it seems to me that c \leq \aleph_1. \aleph_1 is the
cardinality of the set of all sets of cardinalilty \leq\aleph_0. Since c
is the cardinality of the set of all subsets of N, which is a subset
of the set of all sets of cardinality \leq\aleph_0.

What has never been proven is that c=\aleph_1, although it is widely
suspected.

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Dr. Russell Standish Director
High Performance Computing Support Unit,
University of NSW Phone 9385 6967
Sydney 2052 Fax 9385 7123
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Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks
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Received on Tue Jul 13 1999 - 21:41:46 PDT

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