New from @DavidKButler https://davidkbutler.xyz/2026/03/24/three-types-of-infinity/ David includes a disclaimer to ward off people complaining, but I see nothing to complain about. Here's some thoughts it gave me. The use of ∞ to refer to the location at the (positive) end of the number line is a very nice way to put it. If you think of convergent sequences in say metric spaces, the "infinity" point of a sequence is its limit. And the "abstract convergent sequence" (or the "free" or "walking" convergent sequence) is often denoted ℕ ∪ {∞}, with the topology that any increasing sequence converges to ∞. The element ∞ in a convergent sequence in a metric space maps to the location that is the limit of the sequence. You can do a similar thing with the real line, getting the extended real numbers, and convergence of functions as you head towards ∞, say if there's a horizontal asymptote.