Re: An uncountable countable set

In article <452032b9@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Virgil wrote:
In article <45201554@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Virgil wrote:
In article <451df41c@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Virgil wrote:
In article <451dd1f2@xxxxxxxxxxxxxxxxxxx>,
Tony Orlow <tony@xxxxxxxxxxxxx> wrote:

Virgil wrote:
Are you saying that aleph_0 naturals only require
ln(aleph_0+1)/ln(2)
bit positions?
Not at all. I am talking about indvidual natural numbers as members
of
N, ,not N itself, which is not a member of N.
And also for every set of contiguous naturals starting at 0 EXCEPT for
N. Why EXCEPT for N?

For the same reason that a paper sack holding oranges is not an orange.

A set is a sack? It is nothing besides the elements it includes.
A set is a container, and is not one of the objects that it contains.
It is nothing more or less than its contents.

It is determined uniquely and entirely by its contents, as stated in the
axiom of extentionality.

So we agree. There is nothing besides the members.

To say that it is completely determined by its members is not to say
that it "is nothing besides its members". If it were nothing besides its
members we cold not give it a name as a thing of its own.
.

Relevant Pages

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  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... For the same reason that a paper sack holding oranges is not an orange. ... There is nothing besides the members. ... So, it is completely determined by its members, but that's not all there is to its determination. ...
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  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... I am talking about indvidual natural numbers as members of N,,not N itself, which is not a member of N. ... That does not tell me anything about which, if any, actual computers deal with infinitely long strings of binary digits. ... Then it is irrelevant to infinite strings. ...
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  • Re: An uncountable countable set
    ... Tony Orlow wrote: ... I am talking about indvidual natural numbers as members of ... Then it is irrelevant to infinite strings. ...
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  • Re: infinity ...
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