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Beehaw decides: what is the set of all genders?
(strawpoll.com)
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A finite number of genders will be experienced by people, but there are an uncountably infinite number of genders.
The set of genders is like the real number line. You can throw a dart at it and pick out a new gender for every person, but you will never be able to throw enough darts to exhaust the set, even given infinite time.
Some people may even have a gender experience variable over time, maybe repeating cyclically, or maybe more or less randomly jumping across a set, or maybe sliding across a real section, or maybe sliding in multiple dimensions.
If we were to define gender as each person's "gender experience", the number would be g∈ℕ, since the number of people is going to be finite.
However, if we try to define a "gender experience" as a function of common genders, then g:[f(n∈ℝ),...], making it an uncountable infinite.
Interesting paradox: finite as long as one doesn't count them, but uncountable infinite as soon as one tries to.