Set theorists claim that all rational numbers can be indexed by all natural numbers. In § 533 I have shown not only that every natural number n fails but even that with increasing n the number of unit intervals of rationals without any rational indexed by a natural less than n increases without bound, i.e., infinitely. Since nothing but finite natural numbers are available for indexing, and provably all fail, this task cannot be accomplished.
I don't know what goes on in the heads of matheologians. But I know that it is deliberately contradicting the magnificent, powerful, and, for all non-matheological purposes, extremely useful mathematics of the infinite that has been devised by Euler, Gauss, Cauchy, and Weierstrass.
Rational arguments to straighten these matheological assertions are not available.