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From: wjafyfe@watmath.UUCP (Andy Fyfe)
Newsgroups: net.math
Subject: Re: Any number as infinite series
Message-ID: <11227@watmath.UUCP>
Date: Thu, 31-Jan-85 21:12:38 EST
Article-I.D.: watmath.11227
Posted: Thu Jan 31 21:12:38 1985
Date-Received: Fri, 1-Feb-85 01:14:59 EST
References: <17957@lanl.UUCP> <28200048@uiucdcs.UUCP> <1088@aecom.UUCP> <385@hou2g.UUCP> <11209@watmath.UUCP> <6909@watdaisy.UUCP>
Reply-To: wjafyfe@watmath.UUCP (Andy Fyfe)
Organization: U of Waterloo, Ontario
Lines: 19
Summary: 

In article <6909@watdaisy.UUCP> ndiamond@watdaisy.UUCP (Norman Diamond) writes:
>Algorithms are supposed to execute in a finite length of time.

Sigh.  Semantics.

The book "An introduction to the General Theory of Algorithms" (Machtey
and Young) defines an algorithm as "a recipe or specific set of rules or
directions for performing a task".  Nothing about time.  The word 
"finite" is particularly interesting, as the guarantee of termination
was the condition we gave up (over the ability to enumerate programs)
to get the effectively computable functions.  (A bit of CS is creeping
in here, but math-types don't worry too much about finiteness.)

In any event, I thought the result was quite nice, and, at first,
unexpected.  Wonder what Norman would have thought had I merely 
given an existential "pseudo-proof-overview"!

--andy fyfe		...!{decvax, allegra, ihnp4, et. al}!watmath!wjafyfe
			wjafyfe@waterloo.csnet