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by dullcrisp
430 days ago
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Well you did say you were okay with set intersection being partial (or I guess also set difference for the more direct analogy). Maybe not everything needs a solution. (Plus we’ve just gone from division being partial to subtraction being partial…but when I say that I begin to suspect that this argument has been made a lot before and we decided that the negative numbers get to stay. I don’t have anything against them personally but they’re probably less natural than the empty set being a set.) I might be reading too much into what you’re saying about the empty set though and you just mean we could use the word “set” to mean “non-empty set” and then say something like “set-theoretic set” to mean what we now mean when we say “set.” But that sounds like a mouthful. |
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Good point!
> I don’t have anything against them personally but they’re probably less natural than the empty set being a set.
An interesting idea, which history supports: 0 was considered as a number before negative numbers were, and we still usually consider only "natural sets" and not "negative sets" (except for Schanuel: https://doi.org/10.1007/BFb0084232).
> I might be reading too much into what you’re saying about the empty set though and you just mean we could use the word “set” to mean non-empty set and then say something like “set-theoretic set” to mean what we now mean when we say “set.”
Right, or a different word entirely, just like we refer to 1 only as a number that's not prime, not as a "number-theoretic prime." But, anyway, the analogy was just the first one that sprang to mind; it doubtless has many infelicities that could be improved by a better analogy, if it's not just a worthless idea overall.