Conversation

Owen Biesel
@owenbiesel
Did a double take at "[the unique function from the empty set to itself] is not constant", but of course you're right! It's only locally constant.
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Lynn
@chordbug
I suppose for *most* functions X → Y, the definitions ∃y: ∀x: f(x)=y and ∀x: ∀x': f(x)=f(x') are equivalent, but the ∅→∅ function is “vacuously constant” by the second and “trivially non-constant” by the first… is one of these definitions vastly better/more “natural”?
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QC (in Berlin 7/29-??? w/ COVID 😷)
@QiaochuYuan
a clean categorical definition of "constant" is "factors through 1" and the empty function 0 -> 0 doesn't said a simpler way, and similar to "a connected graph has exactly 1 connected component," a constant function is a function that takes exactly 1 value
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