Mathematics

Is 0 and infinity the same thing or are they direct opposites?

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Pretty clearly, zero and

Pretty clearly, zero and infinity aren't the same thing. For example, the number of prime numbers is infinite and (therefore) definitely not zero.

But I'm not convinced that zero and infinity are opposites either. (I'd be more inclined to say that negative infinity and positive infinity are opposites.) One reason is this: "zero" and "none" are often synonymous, as in "I own zero unicorns; I own none." The opposite of "none" is "all" (whereas the contradictory of "none" is "some"). But "all" and "infinitely many" are not synonymous: for example, even if we collect all the grains of sand in the world, we will collect only finitely many grains.

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