Question: "Holder 1 was in the corner here, holder 2 to the right of it, and then diagonally up and left was holder 3, holder 4 was just above it, and then I kept numbering by going diagonally back until I was at the right of holder 2, and so forth. But then over time, I got tired of zig-zagging back and forth from the corner to find a slide and decided to use array numbering instead. Besides, when we started, there were the same number of slides as samples, and now there are way more samples than slides-not everything we need to store is studied by me, but everything I study has a corresponding sample in Storage."
(a) Add array numbering to Figure. What bijection does this suggest (in particular, what sets are involved)? And what interesting cardinality fact can you thereby deduce?
(b) Find a surjection from array numbering to the rational numbers Q. (Why is this not an injective map?) What surprising and interesting cardinality fact does this suggest?
(c) The taxonomist says that there are more samples than slides, but you know that there are |N| samples (because the sample drawers are numbered) and |N| slides (because these slide holders used to be numbered). What gives? (How can both statements be true?)
