> The set of positive rational numbers that is less than the natural number n > and has not been enumerated by the first n natural numbers grows with n.
The cardinality of those sets are all equal, and those sets may be easily bjected with each other and each bijected with |N.
> It is s impossible eneumerate all rational numbers
That may be so within WM's wild weird world of WMytheology, but outside of that WMytheology it only requires a slight bit of mathematical talent.
> i.e., to remove all > rationals from the state of being not enumerated to the state of being > enumerated.
There have been constructed many surjections from |N to |Q and many injections from |Q to |N, every one of which proves WM totally and idiotically wrong in his claim above!
Consider this simple INjection from |Q to |N: 0/1 -->1 Every member of |Q has a representataion as m/n where m is an integer, n ia a natural and they have no ntural number common factor other than one
so let 0/1 -->1 m/n --> 2^m*3*n -m/n --> 5^m*7^n
This maps every rational to a different natural so injects |Q into |N, thus bijects a subset of |N onto |Q and extends easily to surjections of |N onto |Q.
