Re: Existence of reals and observation of them

In article <2978489a-fcdb-40f8-9c6d-fdae10e112f9@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> Venkat Reddy <vreddyp@xxxxxxxxx> writes:
On Dec 13, 6:12 am, "*** T. Winter" <***.Win...@xxxxxx> wrote:
....
No. You only cannot get there by counting. With counting you never get
past the natural numbers (which are, by definition, finite).

Alright, the "size" or cardinality of the set of natural numbers is
what we call "infinite", but none of its members is actually infinite.
Did I get that right? Then I have two newbie questions agian.

1. Though every member in the set of natural number is infinite, why
do we have its cardinality as infinite? (The largest number is
supposed to represent its cardinality, right?)

I think you meant "finite" the first time. But what about the set of
natural numbers that has no largest number?

2. Doesn't a set need to have its bounds defined well? If there is no
right bound, then the brace on the right for the set {1,2,3,....} does
not seem to make sense to me, and I wonder if we still call that a
set.

Yes, we do call that a set. The contents of a set are given (in
general) by description. So N = {n | n a natural number} is a perfect
definition of an infinite set.

Basically, it is the problem in defining "all" natural numbers. The
language meaning of "all" demands well-defined bounds.

What do you *mean* with bounds here?
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
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