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Lester Zick wrote:
> On 30 Oct 2006 19:47:06 -0800, "Randy Poe" <poespam-trap@xxxxxxxxx>
> wrote:
>
> >
> >Lester Zick wrote:
> >> On 30 Oct 2006 10:46:23 -0800, "Randy Poe" <poespam-trap@xxxxxxxxx>
> >> wrote:
> >>
> >> >
> >> >Lester Zick wrote:
> >> >> On 30 Oct 2006 08:34:21 -0800, "Randy Poe" <poespam-trap@xxxxxxxxx>
> >> >> wrote:
> >> >>
> >> >> >
> >> >> >Lester Zick wrote:
> >> >> >> On 28 Oct 2006 12:54:51 -0700, "Randy Poe" <poespam-trap@xxxxxxxxx>
> >> >> >> wrote:
> >> >> >"There is a least integer" and "there is a least real"
> >> >> >are both false.
> >> >>
> >> >> They are?
> >> >
> >> >Yes. If you disagree, perhaps you can name me the minimum
> >> >element of the sets Z and R.
> >>
> >> Or perhaps you can show us how it is "there is a least integer" and
> >> "there is a least real" are both false since it's your contention not
> >> mine.
> >>
> >> >> Perhaps you should take that up with theologians then.
> >> >
> >> >We are discussing mathematics. In the mathematical objects
> >> >called "the set of integers" and "the set of reals" there is no
> >> >least member.
> >>
> >> Well perhaps you can just prove that since it's your contention not
> >> mine?
> >
> >Why, do you think that there's a least integer? What,
> >around -1000?
>
> If 1 is an integer then 1 would be least would it not?
No, 0 is an integer with the property 0 < 1.
-1000 is an integer with the property that -1000 < 1
-100000 is an integer with the property that -100000 < 1.
There are many integers less than 1.
>
> >Proof:
> >A least member x0 would have the property that
> >x0 <= x for all other members x.
> >
> >Let x0 be any integer. x0-1 is also an integer, which is <x0.
> >Thus x0 can't be a least member.
> >
> >Similar argument for x0 being any real.
>
> Not if the integers under discussion are positive:
When we say "the least member of the set of integers" they
are not all positive, since the set of integers is not all positive.
When we say "the least member of the set of POSITIVE
integers", they are all positive.
> is 1 an integer? Is it positive or negative?
It is a positive integer.
But it isn't the smallest member of the set of integers.
> It certainly isn't negative unless so stated.
> Ergo it is not negative nor are integers negative unless explicitly
> qualified. You make one propositional logic error then try to sneak in
> an implicit qualification to justify your original error.
Eh? How is it an "implicit qualification" to mean "the set
of integers" when the set specified is "the set of integers"?
Wouldn't be adding the word "positive" when it is left out
be considered adding a qualification that wasn't present?
How exactly does the "set of integers" have "implicit
qualifications" that "the set of positive integers" doesn't?
What additional restriction is added to Z+ to make it Z?
- Randy
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