Are genders finite? If not, are they countable?

Is equality of two arbitrary genders decidable

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@jordyd A Brouwer-style counterexample showing gender is undecidable:

We know that people can realize they are trans only after they have read a specific text. Choose a function f denumerating all texts, and define g : ℕ → ℕ as g(n) = # vald proofs of the Riemann hypothesis in the set {f(0), ..., f(n-1)}. Note that g is surjective iff RH. Now consider someone who is listing f(g(0)), f(g(1)), f(g(2)), ... in their head. They will realize they are trans iff RH holds.

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