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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. In my own
opinion the proposition should at the very least read "there is a
smallest integer but no non integer smallest real".
~v~~
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