this post was submitted on 18 Aug 2023
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Philosophy is fun too!
Yes, I think so, especially if the theorem is itself profound somehow. It doesn't even have to be in a theorem, if it has a really simple definition that non-obviously leads to a finite set that would be enough for me in this question.
I'm reminded of an argument I heard once that there are no uninteresting positive reals, because being the smallest such number would itself be interesting. That seems faulty to me, it just means it's a set with no minimal element, which can exist even in an interval. The infimum would have to be 0.
Stepping into linguistics for a moment, have you heard of pragmatics? Not sharing irrelevant information is a common unwritten rule in conversations. I specified it here because someone might incorrectly assume I'm unaware you can build arbitrary sets of natural numbers.