1. If you label each point with its angle as a fraction of a full revolution, but in base 3, and then you consider the subset whose ternary representations don't include the digit 2, it is in an obvious bijection to the set of all real numbers between 0 and 1. However, it's very unevenly spread; there are big gaps.

  2. It has occasionally snowed in Uruguay. We debunked this very map just a few weeks ago. It turns out that the first ever World Cup was held in Montevideo (in the 30s maybe?) and it snowed that day.

  3. “Before” refers to the clause, not just the verb.

  4. I could be wrong, but I think OP already knows, intuitively, that the sentence is correct, but wants to understand formally how it works.

  5. Churn.. I'm not sure how that would be good. When it takes months and far-right party support to form a cabinet, that will fall under disagreements after another few months, it seems rather dysfunctional to me.

  6. Well, I don't know a heap about the Netherlands, and if you say you're disappointed in your government, of course that's not an argument I can win! But I think that frustration and visible inefficiency might be partly just the flipside of the compromises inherent in genuine democracy.

  7. I agree with your point about democracy and compromises, but I indeed don't see it working well in my country.. If you want to have a compromise, you need to have some amount of agreement. In our political system, 50% needs to be on board.

  8. I spent some years in NZ, and was there (and a voter) when they introduced proportional representation. I think they have German-style threshold too. Generally there's a lot of negotiation between the parties in the few days after an election, and two or three join together to add up to >50%, but they have to find points of agreement. I think it generally works pretty well (though of course people complain).

  9. But isnt know infinitive in this example too? "To" Is just omitted, no?

  10. Yes, 'know' in 'he can know' is called a bare infinitive.

  11. It isn’t noun/verb, but it’s one of my biggest pet peeves:

  12. "Maybe" vs "may be" is another non-noun-verb one that beginners sometimes mix up.

  13. The pattern goes deeper than that, because they do not sound perfectly identical:

  14. Quite right. That's known as the "primacy of speech."

  15. Yup. In an uncompressed audio format like .wav, every bit combination is valid, so you can take the file size in bytes, multiply by 8 to get bits, and raise 2 to that power.

  16. Yeah, I forgot about the header. Good point.

  17. ah that makes sense, I remember learning that "to teach" takes the accusative twice in ancient greek, but I never thought about that kind of thing in English since it has few inflections

  18. Does it? Like "Alice (nom) teaches Bob (acc) linguistics (acc)"? That seems unnecessarily confusing, if Greek still has six cases. I would have thought Bob would be dative.

  19. I'm not really sure what I thought. I studied Classical Greek a tiny bit in the 80s, and haven't really thought much about dative since then. Wikipedia's first sentence about it says that "the dative case ... is a grammatical case used in some languages to indicate the recipient or beneficiary of an action." That's how we often conceptualise teaching, right? (Probably too much so.)

  20. I mean, the python syntax is great, but the ?: ternary operator is not really harder to use or remember.

  21. There's some sense to what you're saying, but then again, what comes first in an if/else statement, the true block or the false block?

  22. Totally. That's the point of my middle paragraph.

  23. No importa donde dan a luz? Mis hijas no tienen US ciudadania; tengo, pero mis hijas son de NZ.

  24. You have some great advice already, but one things that hasn't been mentioned is to listen—like, really listen—to a number of your favourite songs, and figure out how they are structured. What makes the energy build? What signals the change into the chorus? Is there a bridge? Et cetera.

  25. I don't really understand what you want to do. It seems like an item is evil if it has the most bananas, and good if it has the most apples? But that doesn't apply to your second example.

  26. Maybe the idea is to split the list at the median apple-to-banana ratio? I agree it's not very clear.

  27. Well a square-free number is one with no repeated prime factors; is that what you're after?

  28. I'm currently living in my third country and have never informed any "registration offices."

  29. Three times more than B is more of a layman wording and can mean multiple things. The better wording would be three times B which answers your question.

  30. Yeah I totally agree; some people will interpret this one way, and others the other way. I taught maths for many years, and had many international students. I had to learn to steer well clear of any ambiguous verbiage.

  31. Yeah kiwi here, I’ve had plenty of pies with cheddar but they were all meat-based. I’m kings struggling to picture it with the sweet crust pastry but I guess I’ll give it a go next time?!

  32. Ha!! I only heard the term “hand pies” a couple of days ago in the discussion that lead up to that post.

  33. Same! That was hilarious. Perfectly reasonable name for them, but ... it just sounds so ridiculous!

  34. I'm pretty sure you'll find it a lot easier to start with QED before worrying about nucleons and Higgs particles.

  35. That all sounds reasonable from what I've understood so far.

  36. Although I can understand pretty much none of this, it's definitely refreshing to hear songs in other languages, and of course the emotion comes through strongly anyway. I really like it. Great singing. The chords have a lot of harmonic momentum (if that's a thing). It might be good if the arrangement got heavier as the song progressed, but you're probably already planning that.

  37. It sounded as though you thought Kentucky was a town or small city.

  38. There are 20 cities in China with a similar population. Do you know all of them?

  39. I'm in bed now, and it doesn't look as though we're gonna change each other's ideas. Enjoy your day.

  40. The horror ballads sounds really fun. I wrote a rock musical at one point, but eventually it kind of fell apart, but there are still a few remnants of it as one or two (or 3) songs survived. Those songs came incredibly organically, but I starved it and never saw it through.

  41. Yeah, I'm really keen to do a musical one day! When I retire, if not sooner, I'll take a crack at it.

  42. Terribly click-bait title, but for some reason I clicked it, & it's pretty interesting. The idea is to use octonions to describe symmetries in physics.

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