Javier
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 May 1 comment What do I conclude if I found the eigenvalues of a matrix, then noticed that one of those eigenvalues resulted in a zero eigenvector? There is a nonzero eigenvector; you must have made a mistake somewhere. Mar 2 comment Correct set notation for “all integers which are not multiples of 7”? Don't forget about the simplest one: $\{ x : \text{x is not a multiple of 7} \}$. Dec 25 comment What is the limit of $f(x)=\lim_\limits{n\to \infty}\frac{x^n}{x^n+3}$ when $x$ tends to a certain point? Please don't write things like $x^n = \infty$. Dec 7 comment How to determine if an equation is algebraically solvable? I know that. What I tried to say is that just because a polynomial is of degree $> 4$ doesn't mean it isn't algebraically solvable, only that there is no general solution for all polynomials of that degree. Dec 7 comment How to determine if an equation is algebraically solvable? So $x^5-1=0$ doesn't have a closed form solution because it has degree 5? Oct 9 comment Why do we use square in measuring a qubit with probability? @HamedBaghalGhaffari: Whether or not it's an advantage is irrelevant; the reason we use the squares is that this is how the world works; the laws of physics, which are found from experiment, say so. Sep 30 comment Different ways finding the derivative of $\sin$ and $\cos$. Do you mean you define $\cos$ and $\sin$ as the real and imaginary parts of $e^{ix}$, or the other way around? Aug 22 comment Proof for parallelogram law of vector addition Vectors are a purely mathematical construct. You seem to be asking about the superposition principle, which is the physical fact that forces add like vectors. Don't get it backwards! You seem to be implying that vectors add like they do because of the superposition principle, but it's the other way around: we represent forces with vectors because addition of forces is just like addition of vectors. In any case, I think you should make your question clearer, because apparently no one understood what you were asking. Aug 22 comment Where does this sequence $\sqrt{7}$,$\sqrt{7+ \sqrt{7}}$,$\sqrt{7+\sqrt{7+\sqrt{7}}}$,… converge? This is fine if you've proved it converges, but I'm not sure OP has done that. Aug 22 comment Proof for parallelogram law of vector addition Two things. One, this is a mathematical question, so experimental evidence is not really a proof. Second, how do you define vector addition? Aug 11 comment Rigorous treatment of expressions with differentials in physics books Something to note, more or less echoing what littleO said, is that while sometimes this kind of thing can be formulated more rigorously using derivatives or differential forms or whatever, I find that thermodynamics is an area where it helps to think of differentials as really small quantities instead of a more formal alternative. Aug 8 comment What is this expression means? $\sin^{-2}x$ @MichaelGaluza: Some people use $\sin^{-1} x$ to mean $\arcsin x$, that's the point. Aug 7 comment Distance covered by integrating the Velocity of a Body Most likely your calculator is set in degrees instead of radians. Jul 31 comment Maximum value of $f(x)=\frac{x^2}{x^3+200}$ over natural numbers It should be mentioned that this works as long as $f$ has only one maximum, too. Jul 29 comment $\int_{-\infty}^{\infty}e^{-\pi x^2}\cdot e^{-2\pi ix\xi}dx = e^{\pi\xi^2}$ Hint: Complete the square in the exponent. Jul 1 comment Transforming matrices using tensor transformations? Well, it cannot be just replacing the coordinates, because the transformation law is telling you that you should multiply by two other matrices in addition to replacing $x$ and $y$ by their polar expressions (which is implicit in the transformation law). Jun 12 comment What are “instantaneous” rates of change, really? (...) With this point of view, the limit is not a process that will never end. Instead, it's an indirect way of specifying (without ambiguity) a number that you couldn't otherwise calculate. Maybe this will help. Jun 12 comment What are “instantaneous” rates of change, really? Maybe you should try not thinking of limits as movement, because then, as you say, you never "get there". Rather, when you see a limit like the derivative, imagine that there is a number that you cannot calculate, but that you can approximate with arbitrarily high precision. This is not some fuzzy thinking that cheats by evading the concept of instantaneous rate of change; if you can approximate a number arbitrarily well, then you know exactly what it is, even if you cannot calculate it "directly". (...) Feb 15 comment Examples of apparent patterns that eventually fail Sorry for being three years late, but I don't see what the deal is with the $\sqrt{163}$ sum. I mean, it's pretty cool, but what does it have to do with the question? Feb 13 comment How is SO(2) compact according to this definiton? MathWorld's definition doesn't make a lot of sense, because usually you can't cover the whole group (or manifold in general) with a single coordinate chart.