Ripheus23

Regarding the concept of a metaindex and cardinalities defined therefrom.

https://math.stackexchange.com/questions/2313576/ordinal-tetration-the-issue-of-epsilon-0-omega has more on the subject.

https://math.eretrandre.org/tetrationforum/attachment.php?aid=222 Wild, it seems the omega hyperoperator might yield values of omega for all 2 ^{omega} n, n equal to or greater than 3.

Errors I've made.

I haven't said this anywhere, not even (directly) on Facebook. I got so distracted by my lack of readiness for the quasi-apocalypse we're going through that it didn't quite seem to make enough of a difference. I thought, "Well, I was told I wouldn't end up having to do anything," and since voila, the world came to a halt without my doing anything... But basically, mid-March, I was so frustrated, angry even, that I got myself worked up to go "make my stand" at the Trident base, I was ready for that, and then ZAM an incomprehensible pain started wracking me. A physical pain, my stomach or intestines or both or what were in knots, I still don't know why, I started throwing up for half a day, so there went my idea of overdosing on my meds in front of the Trident base's gates (my only thought, to sacrifice myself as part of some obscure proof), like if I just threw them up, well... And then the pain didn't go away until days and days later, after the lockdown started in earnest, and though the buses have still been running, although I still could've gone to Trigger Avenue or wherever, and walked the last distance... I didn't have the moral energy to do it. And again, besides, the world had sort of "ended" anyway, hadn't it?

I'll admit to being afraid of dying, or of trying to die. I convinced myself that I would "wake up" in Heaven, to my cat no less, and I was imagining being in Heaven with my cat, like we were in this open field and he was trilling along and I followed him around, giving him the attention I failed to give him in the real world, content that I could be with this little creature who liked me so much... I also imagined following him out of the field, to a little house, I imagined my mom might be there (if she has died of her medical condition by now), and I would be reconciled with her, and maybe Heaven is after the actual end of the world, is "the World to Come" as they say, so then maybe I would go and meet up with other people who were lost along the way of my life, not lost to death like my cat and maybe my mom, but still... Yet in the wake of the plague and the lockdown, and the warnings we had about hospitals getting overwhelmed, I started to think, "No, I won't kill myself, I'll volunteer to work at the hospital, to help out during the crisis. That's how I'll stand up to Apollyon." I even went into my "Dean is so valiant" mode and thought that he would be volunteering, too, and that's how we'd reconnect.

Then the hospital called and told me that they aren't doing the volunteer thing right now, and they weren't getting overwhelmed anyway. So I felt defeated again.

On the other hand, I have never been so proud of my country. That's a strong thing for me to say. But so I saw that people were willing to do the social-distancing thing, regardless of the economic consequences, and even though the plague wasn't cataclysmic, especially not for younger people. But people were willing to try to prevent the elderly and other vulnerable groups from getting mass-infected, so willing, they threw away the naive utilitarianism that it seemed like they might defer to so often, or maybe they'd never really deferred to it that much anyway? So yeah, I was and am proud, of course not only of America, but pretty much the entire world at this point.

It feels like a possible turning point, in other words: again, some kind of end to the world, not the end I spent my life readying myself for, but still. And I still think the Trident ships are demonic, still think I'm in the shadow of Apollyon's throne, and all that, and I still wish I could make a stand, still wish that my own darkened world (my terrible life) would come to a meaningful end, but I don't know what to do. I've gone back over my set-theory analysis again, have had to reevaluate it to some extent as I've learned more, and I have so much more to learn, and though my "proof" of the Continuum Hypothesis still seems solid and all, I haven't been able to do anything with it. I can't even post new questions on the Mathematics Stack Exchange anymore because the ones I already posted didn't have a consistent enough upvote, in fact were often downvoted enough that my contributions to the community are not considered worthy enough of the site for now; so no more feedback on that hand. All the professors I've emailed: no reply.

So on another level, my paranoia is resurging. This might in part be due to medication backsliding, although to be sure my medication wasn't doing anything except making me feel vaguely sicker, ultimately, anyway: more confused, more breathing/blood pressure problems, yadayadayada... But so on this level, I've also started wondering if there's more to the danger of the plague than the governments of the world have admitted, as if either the real danger is still to come, or things are worse than are being reported, or even if there isn't that much of a real danger and governments are taking advantage of the situation to move ahead with some questionable plan that they already had and just needed a pretext to put into effect. I'm so confused, in other words, and still in the position of having to ask myself, "What am I supposed to do about it? Am I supposed to do anything?" And my feelings of defeat continue and intensify.

So on the worst level, I feel guilty, or at least almost guilty, like there is something I should do, that I failed to do, and worse, did the opposite of. I can say, "Well, I really was going to go make my stand, I can't blame myself for an unexpected and overwhelming gut pain knocking me down, in fact I ought to be proud enough (or whatever) that I really would've made my stand had it not been for that pain, right?" But I don't know if that's worth saying, if anything I've intended to do or have done is worth that much. I don't know that anything I've ever done has been worth that much. My sense of social connections is evaporating virtually in total, I meet people and have no expectation of long-term relations with anyone, everything as such is just a wild blur in my mind, like, "Today I know this person, tomorrow I'll know someone else, and so on," which is just killing my sense of reality in general, you know? Like there is no real reality anymore, in a weird way.

Confusion on my part, haha!

https://www.wolframalpha.com/ can be used to check some of my statements about transfinite arithmetic. For example, inputting "aleph 0 ^ aleph 0 ^ aleph 0" yields the same answers as "(aleph 0 ^ aleph 0) ^ (aleph 0 ^ aleph 0)" (but note that if you don't use the parentheses like that, you get a different answer) and also "beth 1 ^ beth 1" yields the same answers as the three-step staircase (thus indirectly verifying that c ^^ 2 = aleph-0 ^^ 3). Now there's no way I know of to use up-arrow notation in Wolfram Alpha, so conversions would have to be manual (conversions for checking, that is), but I think the basic information proofs are still helpful.

Something I didn't emphasize clearly enough: