Re: an important set theory post

On Jul 26, 8:43 am, David C. Ullrich <dullr...@xxxxxxxxxxx> wrote:
On Fri, 25 Jul 2008 06:33:52 -0700 (PDT), calvin
So, omega+1 is merely notation for something that
has a clear meaning?

Uh, yes. The clear meaning has been clearly explained
to you here - omega + 1 is the union of omega and
{omega}.

The 'union of omega and {omega}' means something, but
'omega + 1' doesn't (except as notation), because adding
1 to any infinity yields the same infinity.

If so, then it would seem to me
to be in the same category as the notation, 2^aleph_0,
which stands for 'the cardinality of the set of all
subsets of a set that has cardinality aleph_0.'

Uh, yes, it's in the same category in that both
are _definitions_. What's your point?

They're not definitions, it seems to me, but only
notations.

Infinite powers aren't defined, so 2^aleph_0 means
nothing (except as notation). If one didn't already
know that the power set of a particular set is
the set of all subsets of that set, this notation
would be useless. Similarly, 'omega + 1' would be
useless if one didn't already know that what was
meant was the result of the successor function
applied to omega.
.

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