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

On Sep 18, 1:33 pm, tommy1729 <tommy1...@xxxxxxxxx> wrote:

between every pair of irrationals lies a rational.

and between every pair of rationals lies an irrational.

seems like the set 2n and 2n + 1 ( even and odd integers)

so implies equal density and both countable....

or both uncountable...

Whatever your definition of 'equal density' (or even if you just mean
that between any two distinct rationals there is an irrational and
between any two distinct irrationals there is a rational), you have
not shown any proof from axioms and a specified logic (especially here
where the context is ZFC which is the set of sentences derivable by
first order logic from the ZFC axioms) that equal density entails both
countable or both uncountable.

MoeBlee


.

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