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From: dross@umn-d-ub.D.UMN.EDU (david ross)
Newsgroups: comp.edu,sci.math
Subject: Re: Peano vs Dedekind
Summary: Herman's right
Message-ID: <709@umn-d-ub.D.UMN.EDU>
Date: 22 Jan 89 22:10:56 GMT
References: <2035@water.waterloo.edu>
Reply-To: dross@ub.d.umn.edu.UUCP (david ross)
Organization: University of Minnesota, Duluth
Lines: 26

In article <2035@water.waterloo.edu> ljdickey@water.waterloo.edu (Lee Dickey) writes:
>In article <1088@l.cc.purdue.edu> cik@l.cc.purdue.edu (Herman Rubin) writes
>
>>The Peano postulates (really due to Dedekind) contain the essence of the
>>structure of the integers.     ... [ much more deleted ]
>
>Really?
>
>I thought that the Peano Postulates pertained to counting numbers
>and not to integers, and that they really had been done by Peano.
>
Once you have the natural numbers, the integers are a triviality (in a
sense that can be made mathematically precise)

Peano: Sul concetto di numero, 1891

Dedekind: Stetigkeit und irrationale Zahlen, 1872
	  Was sind und was sollen die Zahlen?, 1888

Dedekind was just less explicit.

-- 
   _  _  _      David A. Ross   (Dept.Math.&Stat.,U.ofMN,Duluth)
  / \/ \/ \     BITNET: dross@umndul THISNET: dross@ub.d.umn.edu
 /  /--/--/     (...all the opinions expressed herein are facts, 
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