Comments on Infinity

-Many paradoxes involving infinity arise from intermixing intensive and extensive metrics. (*--*)
-Certainly an extensive metric of these infinite sets gets no grip on the problem of the Collatz conjecture.
-Presumably, use of an intensive metric (i.e. density, a rational) will do better.
- Two or three *such* paradoxes were encountered in this work and resolved by applying density as a measure.
-Much work revealing problems in infinite sets (e.g. Cantor's dust, a set of zero measure but infinite content) is seated within the continuum of the number line.
-But the Collatz conjecture involves only integers, thus avoiding this trap involving "measure".
-The assertion that the predecessor tree contains all the odd integers on the basis of infinite summations of their densities (which gives 1/2) is grounded in the density measure.
-Summation of the densities of the powers-of-2 multiples of all the odds in the predecessor tree gives 1/2 also.