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

[Terry Reedy]

"michael" <serrano at ozemail.com.au> wrote in message
news:IjA77.97824$Rr4.589251 at ozemail.com.au...
> > 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)?

This is a very subtle question, which I believe underlies much of the
recent heat on this newsgroup.  I was taught (by an algebraist) that Z
is isomorthic to a subset of R but is not the same as that subset
(having existed prior to R).  On the other hand, at least some set
theorists regard isomorphic sets as the same set (which is why there
is only 1 empty set!), which would make the two one and the same.  So
it depends on the meaning of 'set'.

Terry J. Reedy