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About uncool

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  1. uncool

    Triple integral

    This integral isn't meant to be evaluated in a straightforward manner. The solution is a trick.
  2. uncool


    Spydragon: do you understand the reasoning behind the equations you gave for a^2 + b^2 = c^2?
  3. uncool

    Neutrons and Gravity

    That is exactly the opposite of correct reasoning; it reminds me of the "25 dollars" riddle.
  4. uncool

    Ellipse definition confusion

    Any shape made by an angled cross section of a circular cylinder can also be made by an angled cross section of a cone, with the exception of the degenerate case (a pair of parallel lines). It will be an ellipse.
  5. uncool

    Ellipse definition confusion

    While you are correct that there is only one obvious symmetry, it turns out that the equations of the cone and plane result in another symmetry. The conic section (whenever the plane is at a shallower angle than the cone itself) is an ellipse.
  6. uncool

    Ellipse definition confusion

    This description does work universally; it takes a bit of algebra to demonstrate it, but it does work. Ellipses can be seen as cross sections through both cones and cylinders..
  7. The statement that the function is discontinuous is calculus. Additionally, this reverses the usual order of definitions. In calculus, continuity is defined in terms of limits, not the other way around. So this begs the question: how do you know the function is discontinuous?
  8. taeto - the function I described does exist; it's not hard to construct using the axioms. In nonstandard analysis (specifically, the version using Internal Set Theory), it isn't standard, and nonstandard analysis defines limits and derivatives for standard functions (as I understand it).
  9. Dasnulium: I don't think you have ever answered this question. In the system you favor, what would the limit of f(x) be in this case?
  10. I think you have either used standard calculus or assumed your conclusion without realizing it in your paper, by assuming that "r" (which you should more explicitly define than "the two sets of terms as a ratio") can always be expressed in the form "+- b epsilon^2 +- c epsilon^3 +-.../+- a epsilon". More generally: let's say we have the function f(x) = 0 if x is neither infinitesimal nor 0, and 1 if x is 0 or infinitesimal (in other words, if x is smaller than any rational number). What is the limit as x approaches 0 of f(x)? (More on this after an answer)
  11. uncool

    Newton, gravitation and second law

    ...the math is what you provided. You asked how we should understand the equation. What math are you asking for?
  12. uncool

    Newton, gravitation and second law

    You should understand it by realizing that the force is proportional to the square of the distance only if acceleration is being held constant, which is generally an unnatural assumption. Mass being held constant is a somewhat natural idea; acceleration being held constant is not.
  13. uncool

    Spark vs Rank of a matrix

    The statement "the spark of a matrix is zero" expands to mean "There is a set of columns of size zero that is linearly dependent." Which isn't true. Spark of a full rank matrix is something of a convention. Spark increases as linear dependence decreases - and a full rank matrix is maximally linearly independent, so you want the spark to be large, not small. Choosing it to be infinity is likely the best convention.
  14. uncool

    Continuity and uncountability

    1) There is a school/philosophy of mathematics that TheSim is referencing, called constructivism. It is a relatively rare view. 2) To be honest, you don't have the experience, knowledge base, or understanding to deal with the differences between constructivism and the standard view. I would highly recommend that you study the basics for quite a while longer.
  15. uncool

    Continuity and uncountability

    And that's a nice demonstration of what I said. The set of real numbers is not countable, pengkuan.