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Are genders finite? If not, are they countable?

Is equality of two arbitrary genders decidable

@jordyd genders have a field _ [0]func() which prevents equality testing

@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.

@jordyd my programmer brain says yes because they are defined by something

whether equality is useful is another thing, because it might turn out to be something that's unique for everyone, and it's not something you could do today anyways since we don't know what defines a gender, just that it's defined by something

@jordyd genders within this universe are finite unless one person can have infinite genders because there are a finite number of people who can exist between the big bang and the heat death of the universe

@jordyd genders are countable, but because sexualities can be defined as P(G2) where G is the countably infinite set of genders, the set of sexualities is uncountably infinite.

this implies the existence of uncomputable sexualities. in this essay, i wi

@hazel @jordyd
It has been conjectured in the existing literature on the topic (e.g. @hazel, 2021) that the set of genders may be [at most] countable, but recent developments in representation and type theories have led some to privately speculate this may not be the case. In this paper, we develop a novel technique which we will utilise to construct an injective map from the unit interval into the class of genders, thus concluding that the class of genders is in fact uncountable. We then speculate on the open questions of the precise cardinality of this class, as well as the foundational question of whether the collection of genders is, in fact, a set.

@cephie @jordyd I mean I guess the question boils down to "can you construct a gender from a collection of other genders", right? since if so, you can apply something similar to the diagonal argument, in which case it is uncountable

@cephie @jordyd I mean -- is the set of genders isomorphic to the set of strings, which is isomorphic to N? are there indescribable genders?

@hazel @cephie Ftr I don't have any investment in the answer to the original question. I just saw an opportunity to mess w you and I took it

An Apology and A More Earnest Reply 

@hazel @jordyd My sincere apologies if my silly reply has come across as anything else! I was just trying to have a little wordplay fun, and goof around with my thoroughly-honed but largely dormant mathematical writing skills; I don't often get to play games like this anymore, and I appreciate your presenting an opportunity—but I really do apologise deeply if this wasn't actually meant to be a game!

For a more serious reply: in the abstract, I would suggest that the number of genders is, indeed, uncountable (I suspect each experience of gender will never be properly encapsulated via quantitative methods, anyway; but if you twist my arm, I'm sure I could point to quantifiable experiential variables that grow or change in continuous ways (say, e.g., something as simple as marking oneself on the famous (though dubious) gender spectrum (or, more properly speaking in its most commonly presented graphical form, gender interval)), and thus lead into uncountability). But as a practical matter, well… the number of genders is, of course, finite (at least as far as the history of humanity is concerned)—there are only, say, a few billion genders that have ever existed, and only finitely-many more will ever exist before the heat-death of the universe, as far as we know (again, in the realm of human experience).

Sorry again if I've caused any trouble, and I thank you both for your indulgence.

@cephie @jordyd I am being pedantic and joking sorry adjfj

@jordyd if its possible for a single person to have infinite gender- genders are infinite and uncountable.

if not, genders are finite but numerous enough (and complex enough) that they're functionally uncountable.

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