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

[David C. Ullrich]

On 27 Jul 2001 11:30:24 +1000, Robin Garner
<robin.garner at iname.dot.com> wrote:

>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. 

Ah. If that's what you were getting at fine. (From my point of view
the thread started when the subject line changed - the quote above
is at the _top_ of this thread, no previous comments from you at all.
So given the words "strictly speaking" I assumed the words "is not a
subset of" meant literally "is not a subset of", which is really
not quite what you're getting at here... didn't mean to be replying
to posts of yours that I hadn't seen, just to the post I actually
replied to.)

>Robin


David C. Ullrich