Re: Cantor's definition of set

On Fri, 26 Oct 2007 14:58:43 -0700, MoeBlee <jazzmobe@xxxxxxxxxxx>
wrote:


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.

I'm beginning to get the meaning of the word "ignoramus" (in this
context).

Another nice thing concerning the definition of the set of natural
numbers due to von Neumann. We may define for n, m e IN:

n < m =df n e m.

So there's a "natural order" defined on this set. :-)

I'd say this contradicts JJ's claim: "...a collection is indifferent to
order."


F.

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