Re: How can I count a set of numbers if all the numbers are inside the set?

On Oct 16, 2:16?pm, Frederick Williams <"Frederick
Williams"@antispamhotmail.co.uk.invalid> wrote:
John Jones wrote:

On Oct 15, 12:22?pm, G. Frege <nomail@invalid> wrote:
On Mon, 15 Oct 2007 10:17:56 GMT, Frederick Williams <"Frederick

Williams"@antispamhotmail.co.uk.invalid> wrote:

I take it then that you don't know how to count the set of natural
numbers (as one set) ... [John Jones]

There is one set of natural numbers. If you mean, not count the _set_
of natural numbers, but rather count the natural numbers, then there are
aleph_0 of them.

Though it will be hard for any person (except god, of course) to count them
all (in a lifetime).

So we know -in principle- how to do it (namely, one by one);
but it's virtually impossible (for us) to perform that task.

F.

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I am asking how you can count as ONE set, if all the numbers are in
the set?

In that case the number is aleph_0. If by counting you mean the human
activity of uttering the words "one, two, three ..." while pointing at
each in turn of a multiplicity of objects then _that_ can't be done; but
in sci.logic people will take counting to mean noting the existence of a
one-to-one map between the set to be counted and some specially chosen
set.

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I'm not sure if I've been clear about all this. I was asking this:

How can I say that there is ONE set, if, for the set in question, ONE,
itself, is in the set?

In other words, how is it possible to even START to count the members
of a set if ONE is not in the set? 'One' isn't in the set because the
set itself is counted as one set.

.

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