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Newsgroups: sci.math
From: hru...@odds.stat.purdue.edu (Herman Rubin)
Date: 5 Nov 2009 15:41:40 -0500
Local: Thurs, Nov 5 2009 8:41 pm
Subject: Re: Is it possible in ZF?
In article <vzqIm.5300$Xf2.5...@newsfe12.iad>,
Eric Schmidt <eric41...@comcast.net> wrote: >Frank Lovelace wrote: Without using countable choice, how do you show that >> Let A be a set of real numbers, and define a=sup A. Is there any way >> to proof the existence of a sequence {a_n} with a_n in A and a_n-->a >> without using the Axiom of Countable Choice? >A plan that might work is: >Let B be the set of real numbers that are limits of sequences of points >in A. Show that B is closed. B obviously contains A. So B contains the >closure of A, including sup A. B is closed? -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Department of Statistics, Purdue University hru...@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558 You must Sign in before you can post messages.
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