(Check your link to the WolframMathWorld article) > Evidently, not every reader of Hacker News is convinced that infinity is not a number, despite several webs

(Check your link to the WolframMathWorld article) > Evidently, not every reader of Hacker News is convinced that infinity is not a number, despite several websites by mathematically learned people who say exactly that Like impendia said, it depends on the context. To give a simpler example: at elementary school I was told that I couldn't write "2 - 3". Essentially my teacher was saying that numbers less than zero did not exist! She wasn't lying to me. She was telling me that we were working with natural numbers only, and that our operation "-" was supposed to be closed on the natural numbers. In the context of calculus, infinity is not a number. lim(n->c) foo = ∞ is just another way of saying that "foo does not converge as n goes to c". But in realm of surreal numbers (or combinatorial game theory), infinities are first-class numbers. You can add them and subtract them alright! Besides, in that realm ω + 1 is not the same as ω. It is greater than ω, as expected. I can even show you a children's game -- that is, we can teach kids how to play it without ever uttering the words sets and cardinals -- that has positions with such values.