I think of combinatorics as a kind of proto-math. You?https://twitter.com/sigfpe/status/1019694472165089280 …
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Replying to @corepresentable
I think of combinatorics as categorified mathematics - and thus more concrete. The category of finite sets is more concrete than its decategorification, the set of natural numbers... because a natural number is really an _isomorphism class_ of finite sets.
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Replying to @johncarlosbaez
Alas, though, "...the objects that we truly want enter the scene only defined as equivalence classes of specifically presented objects. That is, as specifically presented objects with the specific presentation ignored, in the spirit of 'ham and eggs, but hold the ham.'" (B Mazur)
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It is only the specifically presented objects to which we have direct cognitive access; they alone are concrete. The isomorphism classes to which these objects belong, though appealingly objective, are the exact opposite of concrete.
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