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I don't think that's a satisfactory answer for a layperson. Infinity is a size/quantity, for most people that usually means "number". The reason it's not a number is because it doesn't exist on the real number line, but again I don't think the helps people intuitively understand what's happening.

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I think it does. A layperson scratches their head when trying to think about how to circle the square of "infinity + 1" or "infinity / infinity". Framing infinity as something outside of arithmetic is a starting point for a more interesting discussion of countability and types of infinities. Infinity is bigger than any number, so then how could it be a number?

Um, duh, you tip an 8 over. If it's not a number, why is it made out of a number? /s

There are numbers that aren't on the real number line. i, for one. Omega, for another.

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