Re: RAF: Rational numbers, irrational numbers: each dense in real numbers

On Oct 25, 9:25 am, William Hughes <wpihug...@xxxxxxxxxxx> wrote:
No surprise. C would be an uncountable
strictly decreasing sequence. It is easy to
show that no such sequence can exist.
(The proof is the standard analysis proof that
a sum over an uncountable set can only be finite,
if all but a countable number of elements are 0).

I must thank you and MoeBlee for the proof.

Originally, RAF based his proof of the inconsistency
of ZFC on the assumption that < or > were wellorders
on the set of reals R. Since this is clearly false,
RAF wanted to amend his proof, so that it applied to
a subset C of R such that C is uncountable, yet
either < or > would be a wellorder on C.

Now, of course, we see that this is also impossible.

And so RAF's plan is doomed. Of course, you and
MoeBlee already knew that a long time ago.

.

Loading