Re: Well Ordering the Reals

Tony Orlow says...
>
>imaginatorium@xxxxxxxxxxxxx said:

>> Anyway, perhaps you should do this one as an exercise. About three
>> posts ago I pointed out that your belief in a "natural" lexicographic
>> ordering of leftward infinite digit strings is false. Remember? Because
>> you can't say which of the following (for example) comes "after":
>> ......33003300330033
>> ......47152471524715
>
>Actually, using the mirror approach, so that you consider them as the real
>fractions, since 0.3..... comes before 0.5....., they are quite orderable.

That isn't a well-ordering, as has been pointed out many times to you.
This is an infinite descending chain:

.1111...
.01111...
.001111...
.0001111...
...

(assuming you are using the normal ordering).

>So, what is wrong with saying that .....11111 corresponds to the set
>of all elements which are not in the subsets to which they map, aka
>the entire set?

What is wrong is that it is self-contradictory.
If ...111 is an element of your set, and ...111 maps to the
entire set, then ...111 is an element of the subset that it
maps to.

>This answer seems to have been rejected, but why?

Because it is provably an incorrect answer.

--
Daryl McCullough
Ithaca, NY

.

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