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uncool

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uncool last won the day on September 17 2019

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  1. Let's start with this: "Since the conjecture is correct with n, we have B ≠ Ø." Your definition of B was: "B is also the set of the odd and prime numbers y which qualify the expression y < 2n". How does the conjecture relate to the nonemptiness of B (which, if anything is obviously true - there is always an odd number below 2*n)? It sounds like you're trying to define B based on summing, but you have not done so.
  2. Because the property (a + b)*c = a*c + b*c requires it. Or, to slightly modify what John Cuthber said: if you cancel someone else's debt, you are giving them money.
  3. So how is that n proven to exist in the Actor system? What you're saying reminds me of the fact that e.g. any strictly decreasing sequence of ordinals is, in fact, finite, even though (if the initial value is infinite) it can be arbitrarily long. However, I still don't see what it is about the Actor system that forces the "stop" message to be eventually acted on.
  4. I guess my question is, if the "stop" message can be postponed for an unbounded time, why it couldn't be postponed forever, analogous to the Turing machine algorithm.
  5. Why is one of the computations guaranteed to stop while the other isn't?
  6. That said, curvature of a (near-)circle is supposed to be 1/radius, which in the case of the Earth is (if I haven't made a mistake) 16 in/mi^2. I'm guessing that the source thinks that the deviation from flat is supposed to be curvature*distance^2, rather than half that (similar to how the displacement after constant acceleration from a standstill is not a*t^2, but (1/2) a*t^2).
  7. Um. What? Don't get me wrong, I think the OP is wrong, but this almost sounds like the objection to acceleration in the form of meters per seconds squared because there's no such thing as a square second. "8 inches per miles squared" just means that each mile, the rate at which the Earth "drops away" changes by 8 inches per mile (using an approximation where the surface looks like a parabola). The units of curvature are inverse distance, and 8 inches/miles^2 is inverse distance.
  8. Sorry, I didn't quite read closely enough; replace j in the above with k. When you have an answer for that: I think that you have not understood what is so essential about the complex numbers. They are algebraically closed, that is, any nonconstant polynomial with complex coefficients will have a complex root. For example, the complex polynomial x^2 - i will have a complex root. As such, any "addition" of the type you have constructed will, inevitably, result in some kind of redundancy. In most cases, all that happens is that you essentially come up with something equivalent to "mult
  9. plus or minus (sqrt(2)/2 - i*sqrt(2)/2). Alternatively: if I've skim-understood correctly, you've defined j such that j^2 = -i. In that case, what do you get when you multiply (sqrt(2)*j - i + 1) and (sqrt(2)*j + i - 1)?
  10. I accept that this is an impression, and that I probably overstated with "blatantly". My point isn't simply that Maxine Waters called for violence; my point is that the method in which Pelosi analyzed Waters's statement is very different from the method in which she analyzed Trump's statements. And yes, there are reasons to do so - Trump has been and was blatantly dishonest, and blatantly pandered to white supremacists and conspiracy theorists. But I don't think that someone who can analyze Trump's statements and see beyond the perfunctory "Peacefully protest!" can think that Waters's sta
  11. Before I do, I want to make clear: I do not think of any of this as disqualifying, or even that important. I think of Nancy Pelosi as, for the most part, a pretty typical politician; I think that nearly every politician at her level has similar hypocrisies. For a recent example (that is on-topic): Pelosi's response to Maxine Waters's statement that protesters should get "more confrontational". Maxine Waters said "[...] and we've got to get more active, we've got to get more confrontational, we've got to make sure that they know that we mean business" in response to a question of what prot
  12. Mehh. I'm pretty strongly against Republicans, but there is valid reason to dislike her. She's a blatantly pandering politician who is willing to say things, not because they are true, not even because she believes them, but because they are convenient to the current narrative she wants. In other words, a typical politician. And, in my opinion, not as bad as many Republicans (see: Ted Cruz, Lindsey Graham), but one of the more blatant on the Democratic side of the aisle, if only because of her prominence.
  13. Keep in mind that in one sense, most mathematicians don't ascribe an enormous amount of importance to mathematical foundations, but in another they very much do: The standard place where most mathematicians place the foundations of mathematics is set theory, most commonly in the form of Zermelo-Fraenkel with the axiom of Choice (or ZFC). I say standard because there is quite a bit of work on nonstandard foundations - simply removing the axiom of choice is common; some replace ZFC with Homotopy Type Theory (which is beyond me entirely). I say most because there are some mathematicians that
  14. I don't see how "base 10" makes x^2 = x/x.
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