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## Main Question or Discussion Point

Is infinity merely a mental concept, or is it entirely meaningful and common?

Infinity does not exist in the context of a number system. Example: what would infinity minus 1 be? It's not infinite since no finite number plus one equals infinity. We see that the rules of arithmetic are violated, because we can't subtract infinity from both sides to conclude that -1 = 0, which isn't true.

But at the same time there are for example, infinitely many real numbers between 0 and 1 (there is actually even an infinite number of *types* of infinities; this kind is called Aleph-1).

Infinity does not exist in the context of a number system. Example: what would infinity minus 1 be? It's not infinite since no finite number plus one equals infinity. We see that the rules of arithmetic are violated, because we can't subtract infinity from both sides to conclude that -1 = 0, which isn't true.

But at the same time there are for example, infinitely many real numbers between 0 and 1 (there is actually even an infinite number of *types* of infinities; this kind is called Aleph-1).