The present question is of interest because it is answered in very different ways by different groups (mathematicians, physicists, students, professionals of non-mathematical occupations). I ask here (1) because I have no experience yet with answers of philosophers, and (2) because this question is fundamental for Cantor's set theory, who also published a lot of his work in philosophical journals. With respect to mathematical papers he said: "the fact that my presently written work is issued in mathematical journals does not modify the metaphysical contents and character of this work." [G. Cantor, letter to T. Esser (15 Feb 1896)]
The basis of set theory is the proof of equinumerosity or equicardinality of infinite sets by one-to-one mappings. This tool proves for instance that the natural numbers and the fractions are equinumerous sets: Every natural number has its own fraction as a partner and every fraction has its own natural number.
This surprising result was explained by A.A. Fraenkel who told the story of Tristram Shandy. [Laurence Sterne: "The life and opinions of Tristram Shandy, gentleman" (1759-1767)]
"Well known is the story of Tristram Shandy who undertakes to write his biography, in fact so pedantically, that the description of each day takes him a full year. Of course he will never get ready if continuing that way. But if he would live infinitely long then his biography would get 'ready', because every day in his life, how late ever, finally would get its description. No part of his biography would remain unwritten, for to each day of his life a year devoted to that day's description would correspond." [A. Fraenkel: "Einleitung in die Mengenlehre", 3rd ed., Springer, Berlin (1928) p. 24. A.A. Fraenkel, A. Levy: "Abstract set theory", North Holland, Amsterdam (1976) p. 30]
A shorter and simpler variant is the story of Scrooge McDuck: Every day Scrooge McDuck earns 10 enumerated dollars and returns 1 enumerated dollar. If, as a cartoon character, he lives forever and if he happens to return always the dollar with the least number, he will go bankrupt because for every dollar we know when it is issued.
The question is: Is the latter argument sufficient to conclude that Tristram Shandy will get ready and that McDuck will go bankrupt?