[OT] Number theory [Was: A use for integer quotients]
Robin Garner
robin.garner at iname.dot.com
Fri Jul 27 03:30:24 CEST 2001
ullrich at math.okstate.edu (David C. Ullrich) wrote in
news:3b602afa.930850 at nntp.sprynet.com:
> On Thu, 26 Jul 2001 00:01:15 +1000, "michael" <serrano at ozemail.com.au>
> wrote:
>
>>> But strictly
>>> speaking the Integer 2 and the Real Number 2 are different entities.
>>
>>So strictly speaking, Z (the set of integers) is not a subset of R (the
>>set of reals)?
>
> Strictly speaking yes, but nobody _ever_ speaks this strictly
> (except in contexts like the present).
>
What I was getting at was that the integer 2 (as an element of the ring of
integers) is different to the real number 2 (as an element of a field). As
a real number, 2 has a multiplicative inverse, whereas as an integer it
does not. (and as an element of Z_5 it does etc etc)
As sets (and from the p.o.v. of analysis), Z is a subset of R, but as
algebraic entities there is a distinction.
Robin
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