Re: A simple question?


Proginoskes wrote:
MoeBlee wrote:
Proginoskes wrote:
MoeBlee wrote:
Proginoskes wrote:
What is this well-ordering of the reals, then?

In ZFC, there exists at least one well ordering of the set of real
numbers. [...]

Yes, but no one has exhibited one explicitly. Your post suggested to me
that someone _had_ found an explicit well-ordering of the real numbers.

Hmm, I don't know why my post suggested that to you. I just said that
in ZFC every set is well ordered. I didn't say anything about an
explicit exhibition of anything.

You didn't mention ZFC in the post in question. You said (at 4:36):

For example, the real numbers are not well
ordered, but there is a well-ordering of the real numbers which is not
the standard ordering.

A good question (for the group) would then be: Is anyone working on
describing such an ordering explicitly?

--- Christopher Heckman

Actually, that quote
For example, the real numbers are not well
ordered, but there is a well-ordering of the real numbers which is not
the standard ordering.
came from my post. I meant that such an ordering exists, if one
assumes the axiom of choice. I meant to use this simply as an example
that a set need not be well ordered, even if a well-ordering of the set
exists. A better example is probably the set Z of integers. Z is
certainly not well-ordered (it has no minimal element), but a
well-ordering of Z can be explicitly described. I still want to know
what the "natural" ordering of P(w) is.

.

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