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wtf

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wtf last won the day on February 7

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About wtf

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  1. Thanks for the info. As a suburbanite I'm just getting over the shock of learning that cheeseburgers are made of chopped up dead cows. I had no idea.
  2. The nearest horse is far from where I live. But my point was that horses foal (if you say so); they don't horse. Whereas evidently, lambs lamb. Which I didn't know. Now I'm gonna take it on the lam.
  3. As a child of the suburbs I did not know that lamb could be verbed.
  4. Are you saying that if RH was proven the math community would keep it secret? Did they change the fonts on this site so that the text is so light that I can no longer read it? Probably the same people who are covering up the proof of RH.
  5. Nevermind. @joigus already linked the Motl reference that I was about to post. But there's no one-page proof of RH, I'm sure of that. And if RH had been solved we'd have heard about it.
  6. No, they come to the conclusion that you're a little off. At least I did. Likewise brook, which has a different connotation in standard English, meaning "to stand for or tolerate." As in, "He brooks no difference of opinion." You give the impression of playing games with your own internal language, which detracts from whatever you're trying to say.
  7. "I'm not a conspiracy theorist. I'm a conspiracy analyst." -- Gore Vidal Yes, so how did you get from linguistic imperialism to the fine points of the second-order completeness theorem for Henkin models? Thanks for explaining witcraft. Most English-speaking readers probably took that as witchcraft, which made no sense in context.
  8. Most praiseworthy, and you put my freeloading self to shame. I should mention though that according to Google, Stanford University's endowment is 27.7 billion USD. Now 27.7B and ten dollars 😉 Also I went to Cal, and therefore am required to consider Stanford my mortal enemy, at least one day a year when they play football in a rivalry that goes back to 1892. https://en.wikipedia.org/wiki/Big_Game_(American_football)
  9. You paid ten dollars to download a pdf? When you click on the article it comes up in your browser for free. You don't need to download anything. I don't even see a way to download a pdf, let alone pay for one. I am confused. Anyway thanks for the link. I did go back and read section 9 of the SEP article and did not understand a word of it. It seems to be fairly advanced mathematical logic. But there does seem to be a completeness theorem for "general" models, which is apparently a technical term that lets you get a completeness theorem but has some drawbacks.
  10. The SEP article doesn't have page numbers. Can you please point me to what you're referring to? https://plato.stanford.edu/entries/logic-higher-order/ Early on it says, "The situation changed somewhat when Henkin proved the Completeness Theorem for second-order logic with respect to so-called general models (§9). Now it became possible to use second-order logic in the same way as first order logic, if only one keeps in mind that the semantics is based on general models." Whatever a "general model" is. Maybe I'll read it later.
  11. Yes, it does. I'm not sure what you mean by this. I linked and quoted a SEP article saying there is no completeness theorem for second-order logic. Do you have a reference to the contrary? I admit I'm no specialist on this subject. Or is "yes it does" referring to what your question relates to?
  12. I'll take a run at this. I think the key issue is that there is no completeness theorem for second-order logic. In general the OP's post doesn't mention the key distinctions between first and second order logic. OP should give this a read, perhaps there is some insight to be had. https://plato.stanford.edu/entries/logic-higher-order/ In particular, note section 5.2: "We shall now see that there is no hope of a Completeness Theorem for second-order logic." Ok, that's a funny way of putting it but I know what you mean. Ok. But you are conflat
  13. Ok YOU are the OP. My apologies to everyone for that confusion on my part. NSA is a bit of a niche area of study, it won't do you much good in general. It's an alternate model of the real numbers. You'd be better off studying the standard model first; that is, the real numbers as taught in high school, and their formalization in the undergrad math curriculum as in a course on Real Analysis. I'll leave it under the rock two meters due north of the old oak tree in the park. Make sure you're not followed. There are many math resources on the Web, you should just consul
  14. If this is your interest, you'd be better served by a book on elementary mathematical logic, not a treatise on the hyperreals. The least upper bound property is the defining characteristic of the real numbers. It's important. The hyperreals are deficient in that respect. "Can't be all bad." I'll try not to blush with false modesty LOL. I thought you were the OP but if not my apologies. Like I say I haven't followed this thread and should probably go back into my hidey hole. You drew me out mentioning the hyperreals, which I spent some time looking into a while b
  15. I haven't followed this thread so I don't know the context of your paste of an excerpt from Keisler's 1977 or so book on NSA. What you wrote here is perfectly true, since both the hyperreals and the standard reals are models of the first-order theory of the reals. But in order to construct the hyperreals, you need a gadget called a non-principal ultrafilter on the natural numbers. Such a thing exists only in the presence of a weak form of the axiom of choice. So the logical principles needed to build the hyperreals exceed those needed to build the standard reals. Secondly, the
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