Re: Cantor's definition of set

On Oct 26, 10:58?pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
On Oct 26, 2:45 pm, John Jones <jonescard...@xxxxxxx> wrote:





On Oct 26, 9:37?pm, MoeBlee <jazzm...@xxxxxxxxxxx> wrote:
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

---

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

The number 2 is always generated by an application, so I cannot
propose simply 2. I cannot say 2 is a number and leave it at that. I
must specify, and not simply assume, an application that generates it.

Even if numbers existed in a third Platonic realm as stand-alone real
entities, I would not be able to recognise them as numbers except by
employing an application, like counting. But in that case, I make
numbers myself. So there is no Platonic realm of numbers.

It seems to me that your requirements as to applications and all the
rest is a terrible weight of baggage that is not allowing you to even
walk around to enjoy the ordinary sights and sounds.

A sequence is a certain KIND of set.
There's no conflict in a set being of a certain KIND.

A sequence and a collection are mutually exclusive I would have
thought - a collection is indifferent to order. 'A collection of coins
of increasing denomination' does not establish a relationship between
'collection' and a sequenced 'increase'. The collection of coins would
be quite indifferent as to coin order.-

But a sequence is a certain kind of set that "codes" the order.
There's no conflict in that.

MoeBlee- Hide quoted text -

- Show quoted text -

----

It seems to me that your requirements as to applications and all the
rest is a terrible weight of baggage that is not allowing you to even
walk around to enjoy the ordinary sights and sounds.

I understand the demands made by this particular enjoyment, even my
own enjoyment lies a little to the side of it.

But a sequence is a certain kind of set that "codes" the order.
There's no conflict in that.

In that case, the set should incorporate that code in the name of the
set. So instead of saying 'a set of numbers', I should also include in
the name of the set the application for generating numbers. But in
that case, I simply have an application.

More to the point, isn't a set just a name? and doesn't the name of
the set desrcibe the set precisely? A set isn't a formula.

.

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