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From: devlin@csli.STANFORD.EDU (Keith Devlin)
Newsgroups: comp.edu,sci.math,sci.physics
Subject: Re: Student preparedness
Message-ID: <6920@csli.STANFORD.EDU>
Date: 4 Jan 89 06:17:11 GMT
References: <605@ucrmath.EDU> <6578@killer.DALLAS.TX.US> <19252@shemp.CS.UCLA.EDU>
Reply-To: devlin@csli.UUCP (Keith Devlin)
Organization: Center for the Study of Language and Information, Stanford U.
Lines: 18

In article <19252@shemp.CS.UCLA.EDU> verma@mahimahi.cs.ucla.edu (Rodent of Darkness) writes:
[stuff deleted]
>
>	Speaking of division and "fractions" once had a teacher who
>	said that division and fractions had nothing to do with each
>	other.  To this day I have no idea as to why she said this.
>
>						---TS
Presumably to distinguish between x/y written to denote division
from x/y written to denote a certain rational number. The point
being that you cannot formally define rational numbers as the
result of dividing one integer by another - there has to BE an
appropriate rational number to provide the "answer". It boils down
to a question of what arithmetic operations can be carried out in
various number systems, and how a richer system can be defined
from a simpler one. Saying that division and fractions have
"nothing" to do with each other is thus a bit overstretched, but
the point intended (presumably) seems valid enough.