Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.1 6/24/83; site petsd.UUCP
Path: utzoo!watmath!clyde!cbosgd!ihnp4!houxm!vax135!petsd!cjh
From: cjh@petsd.UUCP (Chris Henrich)
Newsgroups: net.math
Subject: Re: How Many Continuous Functions Are There
Message-ID: <660@petsd.UUCP>
Date: Sat, 12-Oct-85 16:21:24 EDT
Article-I.D.: petsd.660
Posted: Sat Oct 12 16:21:24 1985
Date-Received: Mon, 14-Oct-85 04:28:03 EDT
References: <310@ihnet.UUCP> <10556@ucbvax.ARPA> <3368@pur-ee.UUCP> <656@petsd.UUCP> <3686@dartvax.UUCP>
Reply-To: cjh@petsd.UUCP (PUT YOUR NAME HERE)
Organization: Perkin-Elmer DSG, Tinton Falls, N.J.
Lines: 25

[]
In article <3686@dartvax.UUCP> chuck@dartvax.UUCP (Chuck Simmons) 
writes:
> [quoting some equations of mine]
>Now wait a minute.  (1) Since when is the exponentiation operator
>associative (lines 2-3).  (2) aleph-0 ** aleph-0 is NOT aleph-0.

Murphy made me do it.  Here's a less erroneous version:
>> C ** aleph-0 = aleph-1 ** aleph-0
>>              = ( 2 ** aleph-0) ** aleph-0
>>              = 2 ** (aleph-0 * aleph-0)
                                ^ multiplication not
exponentiation... this rule is valid for transfinite cardinals
just as for finite ones.

>>              = 2 ** aleph-0
>>              = aleph-1.
Regards,
Chris

--
Full-Name:  Christopher J. Henrich
UUCP:       ..!(cornell | ariel | ukc | houxz)!vax135!petsd!cjh
US Mail:    MS 313; Perkin-Elmer; 106 Apple St; Tinton Falls, NJ 07724
Phone:      (201) 758-7288