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  1. >I apologize, I do not understand English well, I speak Russian. From Google Translate: Значит ли это, что ваши идеи зависят от того, как люди изменяют свое поведение?
  2. > it is only important that the country behaves as a native, and not as a stranger, then the value will not flow abroad. So, does that mean your idea depends on human beings altering their behavior? Secondly, although you are presenting the technical implementation details of your idea; isn't the idea itself essentially political? That is, normative. "What should be," rather than based in what actually is. Thirdly, by contrasting native behavior to stranger behavior, are you arguing for some form of nationalism as opposed to globalism? As you know, this is the core issue of the day. It's what the Yellow Vest riots in France are about.
  3. How to make your own programming language?

    "I only have a vague idea of what the syntax should look like right now ..." That would be the place to start. First you figure out WHAT you want to build; then you figure out HOW to build it. Projects that reverse the order are doomed, since you have no basis for design decisions. You don't know what you want so you end up with something else, as they say. So first spec out your language. Doesn't have to be complete in every last detail, but get the broad outlines and main syntactic features nailed down on paper. Then the implementation will be far easier, since you are harnessing tools and techniques to a particular objective.
  4. Continuity and uncountability

    You're entitled to that opinion. You'll have to convince the entire worldwide community of mathematicians, along with all of the physical scientists (biologists, physicists, chemists, ...) whose work is grounded in infinitary math. Biology? Yes. How are you going to replace the importance of differential equations in the life sciences? Are you really going to recast everything in the world that depends on diffEq with the theory of finite differences? A huge intellectual project with ZERO practical payoff. Akin to recasting astronomy by taking the earth to be the center of the universe. It COULD be done with great difficulty, at the cost of making everything incredibly convoluted. But why? I don't disagree that neo-intuitionism is making a comeback via automated proof checking software, but it's a long way from that to overthrowing LEM in mainstream math and logic. But as I noted, you are raising interesting points that would be sensible in their own thread. Denial of LEM, advocacy of constructive math, denial of noncomputable reals (what do you make of Chaitin's constant then? Even in computability theory they prove the existence of noncomputable problems), etc., are all interesting. But you are hijacking this thread to grind your constructivist axe. Nothing you've said bears on the thread topic. Start a new thread titled, "What do you think about constructive math?" or "Down with ZF and the evil Cantorians," or "The hell with Mrs. Zermelo and her pro-Choice views." If you did that we could have an interesting discussion. But in this thread? Just a thread jack by someone pushing an agenda.
  5. Continuity and uncountability

    You're wrong about this. Cantor's theorem is a valid theorem of first-order ZF. It's true in any model of ZF, even a countable model. In set theory we are not required to "construct" anything, as I'm sure you know.'s_theorem Point being (I do hope you understand this subtle point) that even in a countable universe, there is no bijection between a set and its powerset. And the simple and beautiful proof can be appreciated by a high school student. But if you are using Skolem's theorem to resolve pengkuan's issues, this is surely far off the mark. Perhaps a separate thread on Skolem's paradox would be interesting, but in the context of the present thread I can't see how it sheds any light.
  6. Continuity and uncountability

    Completeness is a second order property. You're reading too many Wiki pages and too little actual math. As I'm sure you would understand IF you understood, even in a countable model of the set theory, the reals are uncountable. If you don't understand why that is, you don't understand Skolem's result. Even in a countable model, there is still no bijection between the naturals and the reals. You haven't troubled yourself to reply to my observation that the computable real line is full of holes and fails to satisfy the Intermediate value theorem, making it a poor representation of anyone's idea of a continuum.
  7. Continuity and uncountability

    The constructible real line doesn't satisfy the Intermediate value theorem. Hell of a poor model of the continuum, don't you agree? Contrary to your claim that there are no holes, the constructible real line is full of holes, one hole where each noncomputable real used to be. There are many Cauchy sequences that do not converge. Worst model of the continuum ever.
  8. Continuity and uncountability

    ps -- The larger point is that OP seems to believe that there are natural numbers that are infinite; and can't distinguish between the fact that there are infinitely many natural numbers, but each one is finite. On that basis, I don't think the ordinals are going to reduce the confusion in this thread. If as @studiot says I sounded "vitriolic" my apologies once again. I am staying out of this thread from now on.
  9. Continuity and uncountability

    Oh my. You don't believe in \(\omega + 1\)? Perhaps you meant the smallest non-finite ordinal. And by order, perhaps you meant well-order. I'll leave it here as to not appear to be piling on. ps -- Ok I'll pile on just a little bit more. > So it is fairly easy to see that, for any subset of N (it's ordered recall) if there exists a largest ordinal n then this corresponds to the cardinality of our subset Really? That's fairly easy to see? It's not even true as you expressed it, and I'm not even sure what you're trying to say. The smallest ordinal larger than any of the elements of {2, 4, 6} is 7, but the cardinality of that set is 3. The largest ordinal in the set is 6.I couldn't understand what you're getting at. "If there exists a largest ordinal? There is no largest ordinal. Can you clarify your thoughts please?
  10. Infinite Series Expansions
  11. Continuity and uncountability

    I apologize. I get carried away sometimes. No personal malice intended.
  12. Continuity and uncountability

    I did no such thing. I characterized your error, not you personally. I added detail regarding unrestricted comprehension so readers could Google the relevant facts. What you SAID was garbage. That is an objective fact. Not vitriol. And "I think in pictures, not algebra," is unconvincing coming from someone whom I've seen lay out brilliant technical responses to questions of engineering math. You're not lacking in algebra by any means. you're simply lacking some basics in abstract math. Basics easily studied on Wikipedia.
  13. Continuity and uncountability

    If you're wrong on the facts, admit you're wrong on the facts. Tossing insults doesn't reflect well on your character. Perhaps OP "thinks in pictures and not in actual mathematical facts." Why do you get a pass on a silly statement like that? I've seen you rip through engineering math problems with skill and precision on two forums. I'm curious as to why you don't introspect and say to yourself, "I'm great at engineering math. Maybe I should review Russell's paradox." I know for a fact that when you're working a differential equation you don't indulge yourself in flights of fancy. I'm sure you must agree with this point. You know what you're doing and you solve such problems with authority. If you are a little weak on set theory, you could study up. Not toss insults and claim that flights of imagination are more important than getting the math right. You would never make that argument when you do engineering math. Agreed?
  14. Continuity and uncountability

    Nonsense. Garbage. Wrong. @Studiot why are you doubling down on this error? What is an "entity?" Do you see that you are using unrestricted comprehension, so that Russel's paradox has EVERYTHING to do with this? My God man this is GARBAGE. There is no set of all finite sets. There is no set of all infinite sets. There is no set of all finite or infinite sets. And for exactly the same reason. You can't form sets via unrestricted comprehension. There is no technical term in math called an "entity." You are just making this up.
  15. Continuity and uncountability

    Jeez Louise @studiot, there is no universal set. That's Russell's paradox.