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Lester Zick wrote:
> On Mon, 30 Oct 2006 17:32:40 -0500, David Marcus
> <DavidMarcus@xxxxxxxxxxxxxx> wrote:
>
> >Lester Zick wrote:
> >> On Sun, 29 Oct 2006 15:10:18 -0500, David Marcus
> >> <DavidMarcus@xxxxxxxxxxxxxx> wrote:
> >>
> >> >Lester Zick wrote:
> >> >> On 28 Oct 2006 12:54:51 -0700, "Randy Poe" <poespam-trap@xxxxxxxxx>
> >> >> wrote:
> >> >>
> >> >> >
> >> >> >Lester Zick wrote:
> >> >> >> On Fri, 27 Oct 2006 14:23:58 -0400, David Marcus
> >> >> >> <DavidMarcus@xxxxxxxxxxxxxx> wrote:
> >> >> >>
> >> >> >> >Lester Zick wrote:
> >> >> >> >> On Fri, 27 Oct 2006 16:30:04 +0000 (UTC), stephen@xxxxxxxxxx
> >> >> >> >> wrote:
> >> >> >> >> >A very simple example is that there exists a smallest positive
> >> >> >> >> >non-zero integer, but there does not exist a smallest positive
> >> >> >> >> >non-zero real.
> >> >> >> >>
> >> >> >> >> So non zero integers are not real?
> >> >> >> >
> >> >> >> >That's a pretty impressive leap of illogic.
> >> >> >>
> >> >> >> "Smallest integer" versus "no smallest real"? Seems pretty clear cut.
> >> >> >
> >> >> >You must be joking. I can't believe even you can be this dense.
> >> >>
> >> >> Oh I dunno. I can be pretty dense. Just not as dense as you, Randy,
> >> >> but that's nothing new.
> >> >>
> >> >> >Is 1 the smallest positive non-zero integer? Yes.
> >> >> >
> >> >> >Is it the smallest positive non-zero real? No. 1/10 is smaller.
> >> >> >Ah well, then is 1/10 the smallest positive non-zero real? No,
> >> >> >1/100 is smaller. Is that the smallest? No, 1/1000 is smaller.
> >> >> >
> >> >> >Does that second sequence have an end? Can I eventually
> >> >> >find a smallest positive non-zero real?
> >> >> >
> >> >> >How about the first? Is there something smaller than 1 which
> >> >> >is a positive non-zero integer?
> >> >>
> >> >> See the problem here, Randy, is that you're explaining an issue I
> >> >> didn't raise then pretending you're addressing the issue I raised. I
> >> >> don't doubt there is no smallest real except in the case of integers.
> >> >> But that is not what was said originally. What was said is that there
> >> >> is a least integer but no least real. Now these strike me as mutually
> >> >> exclusive predicates. But then who am I to analyze mathematical
> >> >> predicates in logical terms especially when there are self righteous
> >> >> neomathematikers around who prefer to specialize in name calling
> >> >> rather than keep their arguments straight in reply to simple queries.
> >> >
> >> >I'll probably regret asking, but what the heck. Are you saying that the
> >> >following two statements are contradictory?
> >> >
> >> >1. There is a smallest positive integer.
> >> >2. There is no smallest positive real.
> >>
> >> No. In response to these two propositions I'm simply asking whether
> >> you consider integers real?
> >
> >Yes, integers are real.
>
> As I have no doubt.
>
> >> Or you might try reading what I originally
> >> asked which you pronounced illogical without apparently bothering to
> >> read what I wrote.
> >
> >You wrote, "So non zero integers are not real?". I've no idea why you
> >would think that. It doesn't seem to follow from anything that was said.
>
> The difficulty is that the proposition "there is a smallest integer
> but no smallest real" would seem to indicate otherwise.
Nobody has stated that proposition but you.
Actual proposition: "There is a smallest positive integer".
What you read: "There is a smallest integer."
Do you really see no difference between those two propositions?
You can't find a word present in the first that is absent in
the second?
- Randy
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