Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP
Posting-Version: version B 2.10.3 4.3bsd-beta 6/6/85; site ucbvax.ARPA
Path: utzoo!watmath!clyde!burl!ulysses!ucbvax!usenet
From: usenet@ucbvax.ARPA (USENET News Administration)
Newsgroups: net.math
Subject: Re: How Many Continuous Functions Are There
Message-ID: <10556@ucbvax.ARPA>
Date: Sun, 6-Oct-85 03:59:15 EDT
Article-I.D.: ucbvax.10556
Posted: Sun Oct  6 03:59:15 1985
Date-Received: Mon, 7-Oct-85 05:46:45 EDT
References: <310@ihnet.UUCP>
Reply-To: tedrick@ucbernie.UUCP (Tom Tedrick)
Distribution: net
Organization: University of California, Berkeley
Lines: 6

Since the cardinality of the set of polynomials
mapping R -> R is C, and any continuous function
mapping R -> R is the limit of a sequence of
polynomials (the card of the set of such sequences
again being C), therefore the card of the set of
continuous functions is also C.