@DanielFischer thanks. I do see why it's differentiable, but has unbounded derivative, hence not lipschitz. But uniform continuity? Not trivial to prove
@Ted He's precisely what I was thinking of when I said the music of the words. One needn't understand a single thing he's saying to appreciate it. (I sure as hell didn't try to analyze Finnegans' Wake.)
Hi there do anyone know I to develop $(x_1+2x_2+3x_3)^4$? I know the multinomial theorem and how many coefficients are there. but unlike binomial theorem how do I find each coefficient?
Functions are rules that assign to each $x$ in the domain a real number, @Sab. And we're using the algebraic structure in the range to add, multiply, etc., functions.
I don't know what your course is, @Sab, and I really don't know much stats at all.
Well, probably half is probability and half is application to interpreting statistics meaningfully, which actually is worth understanding, @Sab, even if you want to be "pure."
But I never took such a course. Now I'm more interested than I was at your age.
How about this : $\Bbb Z/2\Bbb Z$ multiplied by $\bigoplus \Bbb Z$ is just $\{\cdots, p^{-2}, 1, p^2, \cdots\}$. Does it make sense to think of $\{\cdots, p^{-n}, 1, p^n, \cdots\}$?
I actually find the proofs in calculus easy so far, but I've not really applied them per say, I just know them. For example I know Rolle's theorem but I'm not sure how I can apply it in a question or what kind of question can be asked around it.
The interesting sort of question, @Sab, of which you can find one in one of my exams, is to apply Rolle's Theorem and the Intermediate Value Theorem to show a certain $f(x)$ has precisely $3$ roots or $4$ roots, etc.
@Ted My hyperbola comment comes from the fact that this group is apparently a symmetry of the classical version of the problem I'm working on. And I know that the motion of the object in that case is confined to a hyperbola in the phase space. So maybe not surprising that the Lorentz group shows up.
@gbox: Seriously I don't understand. Pick any monomial (pick $a$, $b$, $c$) and then figure out its coefficient. There are a lot of 'em to do. In most applications, you care about one particular one.
$L/\Bbb C(z)$ and $L'/\Bbb C(z)$ be galois extensions, $\text{Gal}(L/\Bbb C(z)) \cong \text{Gal}(L'/\Bbb C(z))$. Is $L \cong L'$? I have no counterexample neither any proof using classical galois theory. @PedroTamaroff
