Re: Well Ordering the Reals

In article <MPG.1ddd4db2cd2d268698a6bb@xxxxxxxxxxxxxxxxxxxxxxxxx>,
Tony Orlow <aeo6@xxxxxxxxxxx> wrote:


> An enumeration is simply a listing, although usually with some
> ordering. A well ordering appears to be an ordering such that every
> element is comparable with another in a linear order, and every
> subset has a smallest element. This second criterion seems to be at
> odds with the explicit well ordering of any uncountable set as far as
> I can tell.

And TO has amply demonstrated that he cannot tell much.

The empty set cannot have a smallest element. Well ordering requires
that every non-empty subset have a smallest element, or equivalently,
that the set contain no endlessly strictly descending seqeuences of
elements.
.