From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4808 Path: news.gmane.org!not-for-mail From: "mail.btinternet.com" Newsgroups: gmane.science.mathematics.categories Subject: Re: terminology in definitions of limits Date: Thu, 22 Jan 2009 11:16:38 -0000 Message-ID: Reply-To: "mail.btinternet.com" NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain;format=flowed;charset="iso-8859-1";reply-type=original Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241020186 14928 80.91.229.2 (29 Apr 2009 15:49:46 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:49:46 +0000 (UTC) To: "catbb" Original-X-From: rrosebru@mta.ca Thu Jan 22 22:28:49 2009 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 22 Jan 2009 22:28:49 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1LQBgE-0002NU-Mi for categories-list@mta.ca; Thu, 22 Jan 2009 22:21:58 -0400 Original-Sender: categories@mta.ca Precedence: bulk X-Keywords: X-UID: 29 Original-Lines: 19 Xref: news.gmane.org gmane.science.mathematics.categories:4808 Archived-At: Without getting into discussion of the `game' aspect, I feel category theorists should speak out against the epsilon-delta approach to limits as against the neighbourhood f(M) \subseteq N approach, where the notation easily describes the pictures. The epsilon-delta approach is in terms of measurement of a neighbourhood, i.e. one step away from the neighbourhood, and less actual (I almost wrote `real'!), and students find that step difficult. The utility of epsilon-delta is in terms of calculation, rather than geometry and structure. The `only measurable things are real' approach is based on the notion that numbers are the most important aspect of science, rather than one tool to investigate structure. Ronnie