(First of all, it's possible that in view of the site's byline, this term's naming could seem a bit egotistical. If it's any consolation, the gender came first--those of you who came here from my Wordpress or otherwise have been in my presence for a while might remember my previous nom de plume of Orion Ellis. And besides, things like Mann have been valid surnames for centuries, if not millennia; it's only fair that nonbinary folks get a turn to have their genders as their names every once in a while.)
I'm told that documentation and coining posts of this sort are the way to, if not present one's identity in a more coherent fashion, at the very least forgo typing out the same explanation every time someone asks what it means. Thus, you've presumably come here from either my about page, the library, or a direct link from some conversation or other with me or someone aware of me, at least in this early stage of my establishing this corner of the internet somewhere between a lair and a pneumatic tube stretching forever upward, occasionally dropping incomprehensible scribbles from the heavens. Thus, a summary for those without the time, energy, or interest to read the entire explanation, suitable for an expeditious answer to "what even is this creature's gender anyway":
Cantorgender: A gender identity characterized by its composition from infinitely many other, smaller micro-identities, none of which are inherently linked to each other or in any hierarchy of influence over the presentation of the whole, but rather immutable and innate components of the larger gender gestalt with which the user identifies. From a broader perspective, it can appear very similar to being agender, but don't be fooled--it is both vast and infinitesimal at once.
Before we begin, a warning: here there be math. Not exactly the kind with numbers, mind you, rather more along the lines of philosophy after its discovery of erasers. Luckily, this is also often the kind of math that's best explained by drawing pictures. Consider a line, of some finite length (it doesn't much matter what that length is--the prototypical Cantor set uses the set of all real numbers between 0 and 1, but for convenience of typesetting and divisibility let's take 27 here.)
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Now, get rid of the middle third of that line, which leaves two segments behind at the beginning and end of the original, where each is 1/3 as long as the first one. The ends of those segments remain intact--in mathematical terms, we'd be getting rid of the [closed interval] describing that middle, everything x where 9 ≤ x ≤ 18, which crucially leaves 9 and 18 themselves alone. 9.00000000000000001 is gone, 17.999999999999 is right out, but those exact numbers 9 and 18 are fine. This is what I mean when I say to remove part of the line from here on out, but I won't be explaining it every time to avoid tedium and redundancy, so just keep it in mind.
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⇓
|---------] [---------|
Now, take each one of those segments, and get rid of the middle third of *that*. If you like, you can envision this as a fractal zoom such that this smaller segment is really just the bigger one in disguise, and you're just repeating the first step--this is, in fact, exactly what's happening; if you know your fractals, you might be starting to realize that the Sierpinski triangle and the Koch snowflake can both be constructed by this method. So, the whole thing is now:
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|---------] [---------|
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|---] [---] [---] [---|
You can probably see where this is going by now. Get rid of the middle third of each of those four segments, and we'll have exhausted the limits of our plaintext manner of rendering this.
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|---------] [---------|
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|---] [---] [---] [---|
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|-] [-] [-] [-] [-] [-] [-] [-|
(Note that the brackets and pipes aren't part of the set themselves, they're only there to mark the ends of the segments more clearly. As a consequence, this interferes with the monospace type a bit and results in the whole thing being cumulatively a bit wider than it should be with every iteration. A more accurate representation of this would have the total length of the whole thing being the same all the way down, like so:)
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--------- ---------
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--- --- --- ---
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- - - - - - - -
Of course, we don't have this problem if we're working with something infinite like the real numbers--you can just keep removing those middle thirds as many times as you want, and those leftovers will keep getting smaller and smaller. We can safely say that if you do this an infinite number of times, you'll have infinitely many leftovers that are infinitely small.
It's not just one point, it's uncountably infinitely many points! \*badum-tsh\*
...
Okay, that was a really bad joke. But the message still stands, because that fact, the infinite nature of all those arbitrarily tiny leftovers, is exactly what I mean when describing cantorgender--or at least half of what I mean, anyway. There are infinitely many sub-genders that make up the set that, collectively, someone who's cantorgender experiences as their gender identity. Specifically, if every leftover is an individual sub-gender, the number of them in this set is uncountably infinite, in technical terms (which really just means it's got as many of them as there are real numbers, but the details of this aren't terribly relevant to this metaphor).
You'll also recall (or see again if you look back at the end of the previous section, if your memory is as bad as mine is) that each one of those leftovers is infinitely small.
This is a consequence of the fact that a countably infinite amount (as in, less than the size of the real numbers (since we've left the endpoints of each iteration) but still big enough that it only becomes relevant in ludicrous situations like this) has been shaved off the ends of each segment, leaving only those ends themselves. Remember 9 and 18 from our very first iteration on this grand journey? Those are still in the ultimate result--same with 0 and 27, for that matter, since we never touched the endpoints of that original full-length line. But it's only exactly those integers (and some other decimals that we won't bother to calculate here, but if you really want to then it can be "left as an exercise to the reader", since the capacity to do so myself was burned out of me long ago), in that case--there are hard cutoffs every arbitrarily small distance from them, so those elements (as well as all others in the set) are exclusively single points, in isolation.
As a matter of fact, they're so small that even in aggregate, they can't really be said to "add up" (loosely speaking) to anything at all. In mathematical terms, this is described as the set having Lebesgue measure equal to 0, which is defined in a frankly tedious way that I won't inflict on anyone against their will. For our understanding of gender, this translates to the similarity to agender-ness alluded to in the introduction--there are infinitely many genders, yes, but the contributions of each individual one to the whole are so minuscule in comparison to all the genders that aren't experienced by the subject that really, it's as if there's no gender there at all when dealing with the entire set as a whole.
(Those of you with an inclination towards real analysis or point-set topology might notice that this means the Cantor set is also classified as nowhere dense, which isn't necessarily massively applicable to my own experience of it as a gender and so I haven't elaborated on it here, but it's still nicely evocative just as a phrase on its own merits and so it sounded better than "uncountably infinite, measure 0" for a title.)
(Yes, I am well aware that none of this constitutes anything remotely resembling a QED-worthy proof, but really, is there any other way to end a mathematically-verbose work?)
"But isn't it paradoxical," you say, "to have a single term to describe your identity when the entire point of that term is that your identity is both nondistinct enough as to seem all but nonexistent, and vast enough that its components can't possibly be fully enumerated, as well as minute enough that no one element can possibly be sufficient to describe the whole? Checkmate, transgenders/mathematicians/the sizeable intersection thereof!"
Or perhaps, you say "but gender is by its nature a constantly evolving construct, forever redefining itself in terms of new information, and so many adjacent flavors of it can be equally relevant to one's experience as a consequence of their differing-yet-overlapping levels of scope--how could you ever hope to define it in terms of something so dry and logical and objective as math?"
Or even, "there are so many different possible subcategories of this, though! Surely you need additional terminology for cantorgender-but-never-feminine/masculine, cantorgender-but-with-fluid-contents, cantorgender-due-to-plurality, c--"
In reverse order:
Do I contradict myself? Very well then, I contradict myself. I am large, I contain multitudes. (Walt Whitman)