Infinities come in different sizes. There’s a whole tower of progressively larger “sizes of infinity”. So what’s the right way to describe the size of the whole tower?
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The Geometry of SET
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Talking about the sizes of infinite things is tricky in part because the word “infinite” is often used in two distinct ways — to refer to the sets themselves, and also to refer to the *sizes* of those sets. In what follows, let’s try to keep as sharp a distinction as we can between infinite sets and infinite set *sizes*, because doing so will let me highlight an especially paradoxical feature about infinite sizing that I don’t think gets enough coverage. The technical term for a “size”, infinite or otherwise, is “cardinality”, and I should probably use a term like “numerousness” or “numerosity” rather than “size” because the idea it tries to generalize is the notion of “how many”. Still, I’m going to say “size” a lot in this episode just because it’s easier.
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