|
|
Lester Zick wrote:
> On 30 Oct 2006 19:50:42 -0800, "Randy Poe" <poespam-trap@xxxxxxxxx>
> wrote:
>
> >
> >Lester Zick wrote:
> >> It doesn't? My mistake. So there's "no least real"
> >
> >There's no least real.
> >
> >> but a "least integer real"?
> >
> >There's no least integer.
> >
> >There's a least POSITIVE integer. Is there some reason you
> >keep ignoring the critical word POSITIVE?
>
> I don't ignore it. I considered it as understood
You shouldn't consider it understood. That's plain wrong. When
we say "the real numbers" we certainly aren't restricting ourselves
to positive reals.
> but even if you
> include it above such that you have "there is a positive least
> integer" and "there is no positive least real" you're still stuck with
> the implication that there is a distinction between integers and
> reals.
That's certainly true. There is indeed a distinction between
integers and reals. The integers are a subset of the reals.
In general, a subset A of set B can have different properties.
B could have a least member, and A not. Or A could have
a least member, and B not. This difference does not take
away the subset relationship.
Example: A = {x real : x > 2}
B = {x real: x >= 2}
A is a proper subset of B. B has a least member. A doesn't.
Example: A = {x real : x >= 2}
B = {x real: x > 1}
A is a proper subset of B. A has a least member. B doesn't.
- Randy
|
|