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Article #5386Re: How about SET-SIZE(N) = oo ? Can we have some Terminology back??
From: DonH
Date: Mon, 23 Jan 2012 18:09
Date: Mon, 23 Jan 2012 18:09
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"Graham Cooper" <grahamcooper7@gmail.com> wrote in message
news:c969154e-6619-4057-a5ce-4cbd98bbdd10@y5g2000pbk.googlegroups.com...
On Jan 23, 8:55 am, Transfer Principle <david.l.wal...@lausd.net>
wrote:
>
> Of course, another i-word is significant to this thread: "infinity."
> We see
> that Herc rejects the distinction between countable and uncountable
> that's found in standard set theories like ZFC, and instead proposes
> that all infinite sets have set size "infinity." But the others argue
> that
> the word "infinity" shouldn't be used this way -- one can say that a
> set
> is _infinite_, but not that it has set size "infinity."
>
> I've seen previous threads debate the use of that word "infinity," and
> I
> have a question which I've yet to see answered satisfactorily in any
> of
> the previous "infinity" threads: What exactly does the word "infinity"
> mean in the axiom name "Axiom of Infinity"? An answer to this might
> help settle the debate.
Since me and Jesse skimmed the topic of PreCantorian Infinity,
I might add the question, "Is AOI consistent with Peano Axioms?"
or in this case, PEANO + "e" + AOI
or by the time you do that you may as well be talking Naive Set Theory
or ZFC again which makes the question "how long is an infinite piece
of string?"
Herc
# "How long is an infinite piece of string?"
This can be slightly re-stated to provide its own answer -
"How long is an in-finite (non-ending) piece of string?"
Naive? Or, merely definitional?
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From: "DonH" <donlhumphries@bigpond.com>
Newsgroups: sci.skeptic,sci.logic,aus.science,rec.org.mensa
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Subject: Re: How about SET-SIZE(N) = oo ? Can we have some Terminology back??
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