[OT] Number theory [Was: A use for integer quotients]

[Robin Garner]

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