I made an interesting observation recently, and I think it's not reinforced enough in the teaching of maths: "infinite" and "infinity" have less to do with each other than you would think. "Infinity" is a particular point in a set. "Infinite" describes the size of a set. There's only one "infinity"[1] but there's (infinitely!) many types of "infinite." By application of the Sapir-Whorf hypothesis, this would be easier for people to understand if we used more separate terms for the two concepts.<p>[1] Well, you can have +/-infinity... or you can make it the same infinity at both ends. This is really the only way to go when you deal with the complex plane instead of the real line. But regardless, the point is in topology, infinity can be treated as singular and definite.