Question: Infinitely many field biologists arrive, each with infinitely many specimens. "I'll leave the first specimen in the first drawer. Then I'll put two specimens from the first field biologist in the second and third drawers. I'll move the specimen that was in the second drawer to the fourth drawer, and the specimen from the third drawer to the ninth drawer. Then two more specimens from the first field biologist will go in drawers 5 and 6, and two specimens from the second field biologist will go in drawers 7 and 8. The specimens from those drawers will get moved down further . . . two more specimens from the first field biologist will go in drawers 10 and 11, two more specimens from the second field biologist will go in drawers 12 and 13, and two specimens from the third field biologist will go in drawers 14 and 15. And so forth and so on, including specimens from an additional field biologist in each round of placements, until every specimen has been placed in a drawer or moved to a new drawer."
(a) What is the sample-moving function described in this quotation?
(b) What is the algorithm the Storage Coordinator is using to place new samples?
(c) Will there actually be enough room for all of the new samples? Explain.
(d) What monstrous cardinality fact is hiding here? Make and justify (but don't attempt to prove) a conjecture.
(e) Did you expect that the set of drawers and the set of new samples would have the same cardinality? Why or why not?