Re: Cantor's definition of set

On Thu, 25 Oct 2007 13:37:58 -0700, John Jones <jonescardiff@xxxxxxx>
wrote:


Anyway, if the members of a set are unique, then I would not like to
say that they have anything in common. So if numbers are unique, then
I would not like to say that they have anything in common.

Look, man: if a, b are elements in the set M, then at least they have in
common that they are elements in M; won't you think so? And that seems
to be inevitable.

Actually, if we consider the set w (as defined in set theory) we usually
refer to the elements in w as "natural numbers". Hence any element in w
is a natural number (by definition). With other words, all elements in w
have in common to be natural numbers.

So where's the problem? Don't you like natural numbers? Or do you think
there's a problem with the concept of set? :-o

-----------------

Now let's consider Cantors "definition" again:

"By a 'set' we mean any collection M into a whole of definite,
distinct objects m (which are called the 'elements' of M) of
our perception [Anschauung] or of our thought."

So if we assume that there actually are natural numbers

1, 2, 3, 4, 5, ...

(say in some Platonic sense) we might consider the collection into a
whole of the numbers

1, 2 and 3

(which are definite distinct objects).

Hence let M be the collection containing exactly the numbers

1, 2, and 3.

In symbols:

M = {1, 2, 3}.

Where's the problem?


F.

--

E-mail: info<at>simple-line<dot>de
.

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