Re: Well Ordering the Reals

Tony Orlow says...

>Um, have you looked at the ordering I proposed? The page link is below. It is
>anything but a normal quantitative ordering of the reals. The ordering of the
>set uses the leftmost bits as most significant, whereas in the quantitative
>order the rightmost bits are most significant. In this ordering, every real has
>a successor, and predecessor, except for the first element. So, as an ordering,
>there is no gap in the successorship, which is what I was referring to.

It doesn't matter whether you start from the left or from the right.
The lexicographic ordering of the infinite bitstrings is not a well-ordering.

--
Daryl McCullough
Ithaca, NY

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