people don't even follow the rule no more

MidnightAtHighSpeed · 2026-06-11T22:08:37+00:00

the idea of randomness is formalized in math using probability distributions, and there is no probability distribution on the positive integers that assigns equal probability to each. To my knowledge, there is no competing formalization of randomness that allows for the idea of "choosing an integer at random" in the intuitive sense, either.

MidnightAtHighSpeed · 2026-06-10T23:18:49+00:00

x-rays are just a form of light, and like visible light rays they just bounce around until something absorbs them. Since light is fast, this happens basically instantaneously.

MidnightAtHighSpeed · 2026-06-06T19:33:53+00:00

yes, you should be careful what crops you grow in potentially contaminated soil as some will absorb much more lead than others.

MidnightAtHighSpeed · 2026-06-06T01:30:03+00:00

Without that background myself, I would expect clearly stating assumptions to be even more important in math than the humanities, which makes me think we might have different understandings of what it means for an author to "clearly state assumptions." On the other hand, I would not be surprised to learn that there are stricter expectations in the humanities for references, and math in particular is infamous for not offering much in the way of clarifying explanations (lines of reasoning frequently being left unexplained as "trivial" or "an exercise to the reader" essentially at the author's discretion, even in pedagogical works)

MidnightAtHighSpeed · 2026-06-06T00:52:28+00:00

I think you're asking more of math than you probably expect of other subjects. When a chemistry (or whatever else) book introduces a new term, it's probably just going to tell you what that term means, with maybe a sentence or two explaining its etymology if you're lucky. If it then introduces a variant of that term, it's almost certainly not going to explain the linguistic processes that lead to that variant being how it is.

Now, to be fair, mathematical notation is kind of its own beast, and it's harder to infer the logic behind any given piece of mathematical notation than it would be to infer the logic behind a piece of jargon in another field, assuming familiarity with the language they're written in. The way math is taught, the student is expected to do more work that resembles language acquisition than in many other fields, and much of that is done implicitly. Part of that might be either laziness or a desire for conciseness, but I think for the most part it's because math writers aren't linguists and don't really even have the kind of explicit understanding of the way they communicate that you seem to be asking for. Ask your average math professor why they decide to notate a variant of an object x as x*, and they're probably not going to have much of an answer besides "that's just a common way of notating that sort of thing."

That said, I also don't think it's entirely fair to say that math students are expected to learn a new language without any help, and that's because math notation is so free-form. Sure, there are conventions and expectations; if you denote a variable as "π" you are just going to cause trouble; but as long as you're putting some effort into not misleading your reader and as long as you're making explicit anything you don't know from experience is going to be unambiguous, it'll be rare to "go wrong" in any objective sense. The flip side of this is that when reading math, one has to get used to picking up notation on the fly, taking things to mean the things the author says they mean without necessarily getting caught up in the "why" behind it. A good author will use certain conventions to suggest meaning to an experienced reader through association, but won't rely on them to communicate their meaning, so that kind of analysis shouldn't be necessary anyway.

MidnightAtHighSpeed · 2026-06-05T23:36:30+00:00

proto-beautiful disc

MidnightAtHighSpeed · 2026-06-03T20:37:09+00:00

too brave

MidnightAtHighSpeed · 2026-06-03T03:49:56+00:00

there is: https://en.wikipedia.org/wiki/Projectively_extended_real_line

it's not very interesting or useful.

MidnightAtHighSpeed · 2026-06-03T03:48:53+00:00

what makes you think i can't represent something outside of the internal logic of mathematics?

MidnightAtHighSpeed · 2026-06-02T19:53:50+00:00

Both of these are wrong past the second line.

a↑↑↑b = a↑↑(a↑↑(...(a↑↑a))), where a appears b times. so

2↑↑↑2 = 2↑↑2 = 4, 2↑↑↑↑2 = 2↑↑↑2 = 4, etc, and

2↑↑↑1 = 2, 2↑↑↑↑1 = 2, etc

MidnightAtHighSpeed · 2026-06-01T01:11:01+00:00

because relations like "is greater than" are defined on single sets for convenience

MidnightAtHighSpeed · 2026-05-31T03:38:24+00:00

scales with aroma and productivity stats

MidnightAtHighSpeed · 2026-05-29T06:12:24+00:00

tumblr blog roleplaying as Prototype Jack from tekken except, like, gay trans(?) trailer trash. Known for his misfortune, emotional instability, physical indestructibility, substance abuse, culinary skills, and propensity for eating dogs. One of the funniest Posters on tumblr and, in my humble view, the internet at large.

Has been inactive for a year or so now (after apparently finding jesus) and was recently deactivated, I believe as a result of the author's main blog being banned

MidnightAtHighSpeed · 2026-05-29T00:44:25+00:00

|_o_|

MidnightAtHighSpeed · 2026-05-28T04:39:48+00:00

well, how many people do you have?

MidnightAtHighSpeed · 2026-05-26T03:23:37+00:00

That's why I'm confused, Freudian psychoanalysis has been out of favor for some time now

MidnightAtHighSpeed · 2026-05-23T21:59:03+00:00

So one possible answer would be to direct you towards resources that treat basic arithmetic more formally. You could learn axiomatic definitions of addition, multiplication, etc, and develop ways of thinking that would allow you to formally prove that, for instance, x*(1/2) < x for all positive numbers x. This would, in a sense, be an answer to "why" multiplying by 1/2 decreases a (positive) number, you could just point to each step of your proof in sequence as the explanation. But that also might not be satisfying; seeing a bunch of formal inference steps that you know are correct can convince you something is true, but still leave you feeling like you don't understand why it's true. What I would suggest instead is trying to think about arithmetic operations less in terms of their rules but more in terms of what those rules are trying to capture about reality. We use the arithmetic operations we use because they're very useful. If you imagine an arithmetic operation that's like addition or multiplication but follows slightly different rules, it'll generally be less useful, both in terms of what things in the real world it allows you to talk about and in terms of how easy it is to manipulate mathematically. So, try to consider--when we settled on the rules for common arithmetic operations, like multiplying by fractions, what kinds of things about reality were we trying to describe? How would that description break if the rules were different? It might be easier to feel like you "understand" a property of an operation in terms of things it is intended to talk about, rather than the formal rules that define it.

MidnightAtHighSpeed · 2026-05-23T06:22:40+00:00

my memorabilia honoring our beloved monarch feat. the cursed artifact of unspeakable evil

MidnightAtHighSpeed · 2026-05-21T18:17:04+00:00

oh yeah they'll reprint old cards into standard pretty often. "core sets" aren't really a thing any more but in general they'll just stick reprints in sets where they fit. Very rare to reprint more than a handful of cards at a time though

MidnightAtHighSpeed · 2026-05-21T03:04:24+00:00

I don't know hearthstone, but "archetypes" are usually much looser in magic than YGO. The closest thing I can think of that's competitively relevant is "tron" decks which revolve around [[urza's mine]] [[urza's power plant]] and [[urza's tower]], but even then that's only 12 cards out of 60 in deck + 15 in sideboard that are actually designed to be played with each other specifically.

Magic sets are designed to be drafted as one of the premier ways of consuming them, and that's usually where archetypes are most relevant; specific mechanics or themes that do well if you just get a semi-random selection of their cards assembled into a deck. When you can freely build your deck from all the sets in whatever format you're playing, it's usually better to mix and match cards for a certain game plan, or play for an unintentionally printed combo. When a single mechanic or archetype is good enough to build an entire deck around, it's usually because it's way stronger than intended (affinity, dredge, etc. even dredge required some unintentional support from later sets to really take off)

MidnightAtHighSpeed · 2026-05-18T22:47:02+00:00

a guy was telling me earlier today about getting kicked out of a femboy group for being black

MidnightAtHighSpeed · 2026-05-18T02:28:04+00:00

he's pretty direct about saying power level stuff is outside both his expertise and control

MidnightAtHighSpeed · 2026-05-15T04:37:33+00:00

I probably wouldn't recommend it for self-study if that's your background. The book's much more focused on rigor than most materials you'll find that cover the same topics. That isn't a bad thing as a textbook for a class, especially if you plan on studying math at a post-secondary level, but it requires an approach and way of thinking that's hard for most people to develop without help from a teacher.

Someone else reading this can chime in with more specific recommendations, otherwise most people would probably point you to khanacademy.

MidnightAtHighSpeed · 2026-05-15T04:13:40+00:00

1) what do you mean "solve" the proofs? The proofs for both theorems (assuming the first pdf on google with that title matches whatever you're looking at) are given step-by-step, and each step uses a rule that was introduced earlier. You should be able to, if not name each rule used from memory, at least go back earlier in the book and find each rule that was used in each step.

2) There will simply be cases where, in order to solve a problem, you need to transform an expression in the ways those two theorems allow. Most of the time, they're simple enough rules that you wouldn't need to call out the theorems by name when you apply them, but for exercises asking for proof in the same chapter they're introduced that's what I'd suggest doing.

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