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Topic: Matheology § 210
Replies: 24   Last Post: Feb 12, 2013 1:12 PM

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Posts: 18,076
Registered: 1/29/05
Re: Matheology § 210
Posted: Feb 10, 2013 4:37 AM
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On 9 Feb., 22:09, Virgil <> wrote:

> Does the finiteness of the members of that set establish the finiteness
> of the set itself?

The finiteness of the natural numbers in combination with the constant
difference of 1 establishes that the natural numbers are in bijection
with the initial segments. This together with principle of induction
implies that the sequence 1, 2, 3, ... has no upper threshold. It is
potentially infinite, but it is not actually infinite.
> > > What term or terms does WM want to use for
> > >    "more than any finite number finite levels"?

Potentially infinite.
> > The term is infinity, the limit is the same (improper limit) as of
> > the supersequence 1, 2, 3, ... of 2, 4, 8, ..., denoted by oo.

> Actually, proper grammar, at least in English, requires that the term be
> "infinite" not "infinity"

You are not a native speaker? The noun is infinity. Compare any
dictionary of your choice.

Regards, WM

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