From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/1468 Path: news.gmane.org!not-for-mail From: "Wendt, Michael - SSMD/DMES" Newsgroups: gmane.science.mathematics.categories Subject: RE: stupid question? Date: Wed, 29 Mar 2000 16:48:16 -0500 Message-ID: <2C04611DA826D311A66D00902715763B0760C2@msxa4.itsd.statcan.ca> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 X-Trace: ger.gmane.org 1241017851 31377 80.91.229.2 (29 Apr 2009 15:10:51 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:10:51 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Wed Mar 29 18:44:54 2000 -0400 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.9.3/8.9.3) id SAA09723 for categories-list; Wed, 29 Mar 2000 18:44:48 -0400 (AST) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Received: from zent.mta.ca (zent.mta.ca [138.73.101.4]) by mailserv.mta.ca (8.9.3/8.9.3) with SMTP id SAA17342 for ; Wed, 29 Mar 2000 18:29:01 -0400 (AST) X-Received: FROM smtpshb2.statcan.ca BY zent.mta.ca ; Wed Mar 29 18:29:52 2000 X-Received: from smtpshb2.statcan.ca (localhost [127.0.0.1]) by smtpshb2.statcan.ca (8.9.1a/8.9.1) with ESMTP id RAA23696 for ; Wed, 29 Mar 2000 17:39:03 -0500 X-Received: from smtpsha.iusd.statcan.ca (smtpsha.iusd.statcan.ca [142.205.234.131] (may be forged)) by smtpsha.iusd.statcan.ca (8.8.7/8.8.7) with ESMTP id QAA01014; Wed, 29 Mar 2000 16:57:12 -0500 X-Received: from msxa1.statcan.ca (msxa1.statcan.ca [142.205.234.72]) by smtpsha.iusd.statcan.ca (8.8.7/8.8.7) with ESMTP id QAA00657; Wed, 29 Mar 2000 16:56:25 -0500 X-Received: by msxa1.statcan.ca with Internet Mail Service (5.5.2448.0) id ; Wed, 29 Mar 2000 16:48:10 -0500 X-Mailer: Internet Mail Service (5.5.2448.0) Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 33 Xref: news.gmane.org gmane.science.mathematics.categories:1468 Archived-At: How about the following? f(x) = 0 if x is irrational and f(a/b) = a, where a/b is a fraction in lowest terms Certainly within any open interval, there are rationals of arbitrarily large numerator. For a function that is not bounded above or below, how about: f(x) = 0 if x is irrational f(a/b) = a if b is even f(a/b) = -a if b is odd -----Original Message----- From: M.M. Mawanda [mailto:mm.mawanda@nul.ls] Sent: March 29,2000 4:08 PM To: cat-dist@mta.ca Subject: categories: stupid question? I have been asked the following question: Is it true that any function defined in a real number closed interval [a,b] (there is not a hypothesis of continuity) is bounded in an open subinterval (c,d) of [a,b]? My spontaneous was NO. Unfortunately I cannot find a counter-example to disapproved my answer. Can someone help.