Re: Cantor's definition of set

On Oct 26, 1:29 pm, John Jones <jonescard...@xxxxxxx> wrote:
On Oct 26, 2:59?am, G. Frege <nomail@invalid> wrote:

1,2,3,4,5... is often portrayed as numbers. But aren't they examples
of the signs we use to portray numbers, and aren't these signs simply
arranged in a sequence and not numbers after all? For I cannot use
1,2,3,4 ... mathematically. 1,2,3,4 ... does not occur in any
mathematical calculation. I can find 1, and 2 and 3 and 4 in a
calculation, but in finding them don't I merely find the signs and not
the numbers themselves? What I am saying is, you can't pull a number
out of the application that generates it. It would seem, if this is
true, that a set of numbers is an impossibility.

'2' is a numeral. 2 is a number.

I don't see your difficulty with this.

The second major problem which simply won't go away, is this: A set is
the concept of a particular collection or group.

Maybe you should distinguish between whether it's a concept of a
collection or whether it IS the collection.

At least I have seen
a set described as either a collection or a group. Now a collection
does not support sequence: in fact if a collection could be a
sequence, it would be a sequence and not a collection.

No, that just doesn't follow. A sequence is a certain KIND of set.
There's no conflict in a set being of a certain KIND.

Don't get me
wrong here. I can have a set of sequences, but the the set itself, on
its own merits, cannot support a sequence. I must establish the
presence of a sequence independently of its membership in a set.

I dont' see any reason we MUST do that. We prove that f is a sequence
by proving that it has the property mentioned in the definition of
'sequence', and that definition ultimately reverts to the sole
primitive 'e'.

This,
I advance, is another reason why I cannot have a set of numbers.
Numbers in a collection are like numerals in a sack, like lottery
'numbers'

I don't envy you the knots you've tied yourself in.

MoeBlee


.

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