> On Saturday, 16 August 2014 21:49:10 UTC+2, Ben Bacarisse wrote: > >> > What are the infinitely many elements that the cardinality measures? >> >> The limit does not measure anything, because there is no "final set" for >> it to measure. That is the core of you misunderstanding. > > Nothing? Well, may be. But if we neglect the limit, we are left with > all natural numbers: > Forall n: There are infinitely many rationals without index.
The above is undeniably true (given some details that I am sure apply in this context).
> If there is no limit, then this is the final answer and cannot be > changed.
What sort of mathematics has final answers and answers that can be changed? The above is true. Period. It was true before you wrote it down. It will be forever true (given the same definitions and axioms).
Does the WMglish phrase "the rationals can't be enumerated" simply mean that all bijection from N to Q have the property that "for all n, there are infinitely many rationals without index"? If so, I'll add it the lexicon.