There are some topics that only the most confident pop-mathematics bloggers can avoid writing. The topics are well-covered already. But they are fascinating, and they are accessible, and that is a powerful combination. One of them is the cardinality of infinitely large sets. That we can say some infinitely large sets are the same size, and others are larger, and have something that seems to make coherent sense.
To date I haven’t written that, not exactly. I have come close, though. One of them is from the End 2016 A-to-Z and its essay on Cantor’s Middle Third. It is a scattering of dust along a line segment. It is a set of points which, altogether, cover no length. But there are as many points in this set as there are in the entire real number line. It’s neat to discover. Please consider it.