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I'm just nitpicking, but it's unlikely that the inventors of both had empty set and zero formalized to a degree to make them distinct.
by kreetx 2y ago
I'm just nitpicking, but it's unlikely that the inventors of both had empty set and zero formalized to a degree to make them distinct.
- adrian_b 2y agoWhile the empty set and the number "zero" are distinct concepts, the relationship between them is much closer than between any other sets and numbers. The cardinal numbers are equivalence classes of the sets. For any other cardinal number except "zero", the equivalence class of that number contains a huge number of sets, potentially infinite. For "zero", the equivalence class contains only a unique set, the empty set. Because of this one-to-one correspondence between the empty set and "zero", they may be interchanged in many contexts without causing any ambiguities.
- kreetx 2y agoRight. What I was aiming at was that when someone invents one of these, they are probably thinking about the other, too, without the set theoretic rigor you recite.