Re: an important set theory post

On Jul 24, 9:23 am, David C. Ullrich <dullr...@xxxxxxxxxxx> wrote:
You're really becoming totally unreasonable.
You admit you don't really understand this
and that, all you know is what you were told
in college many years ago, but you continue
to argue when people give you the correct
_definitions_. A cardinal is in fact a certain
sort of set - whether you believe that or not
has no bearing on the facts of the matter.

But I'm reasonable now, because I understand that
each natural number really is a set, and that
each one is constructed using the successor function:

If n is a natural number, then succ(n) = n U {n}.

Also, aleph0 is a set:

aleph0 = {0,1,2,3, ...}
and succ(aleph0) = aleph0 U {aleph0}.

If we define aleph1 = succ(aleph0),
then aleph1 = {aleph0,0,1,2,3, ...}

I'm still working on understanding the minimalist
nature of these things, that aleph0 is the
minimal cardinal greater than any
natural number (called an ordinal now). That
seems intuitive, but I can't prove it yet.
And then I need to understand that aleph1,
constructed above, is the minimal cardinal greater
than aleph0.

But these things are laid out by Halmos, and also
in the other book I have, and in this thread, so
I'm on my way. I just had to get past the block
of resistance to a number being called a set.

Thank you for being so patient.
.

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