I have another blog that doesn't suck. Archive:
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I used to know a guy who, whenever someone said “an infinite number of…” would reply primly with “infinity is not a number”. Which, if you are speaking mathematically, as this guy was, is complete bullshit. As I mentioned elsewhere, “infinity” in mathematics refers to several different ideas. For example, transfinite cardinal numbers. Oops, I said “numbers”. Transfinite numbers are not numbers. Um. I mean, “transfinites are not numbers”. Just because you can add them and multiply them and raise them to powers and they mix together with finite numbers and they are a generalization of finite numbers and the addition and multiplication and exponentiation are consistent with the way thouse work for finite numbers does not mean that transfinites are also numbers! No no no! Think of this analogy. Suppose there was some entity that was halfway between two and three. And suppose we could add with that entity and multiply with it and compare it with numbers and so on. And suppose there was a notation for it, I don't know, something like “!!\frac52!!” or something. You wouldn't consider that strange entity to be a number, would you? I mean, how could you possibly have !!\frac52!! children or !!\frac 52 !! automobiles? Ridiculous.
