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

On Sep 18, 1:00 pm, Virgil <vir...@xxxxxxxxxxx> wrote:
In article <1190143281.701445.175...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
"Ross A. Finlayson" <r...@xxxxxxxxxxxxxxx> wrote:

In ZFC, with standard definitions of the real, rational, and
irrational numbers, let p_i be an irrational number between zero and
one for i from a suitably large well-ordered index set X.

I very much doubt that Ross can exhibit such an X explicitly.


Any ordinal equivalent to the set of irrationals would do. (Ordinals
are sets of lesser ordinals.)

With the
well-ordering of the index set, let the i'th element p_{i+1}

How is it that the ith element is not p_i??

[Remaining nonsense snipped]

Ah, mea culpa, "{i+1}'th".

Ross

.

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