Javier
Reputation
3,538
Top tag
Next privilege 5,000 Rep.
Approve tag wiki edits
 Oct 11 answered Geometric significance of $\sqrt{A^2 + B^2}$ in general equation of line, if any? Oct 11 revised Geometric significance of $\sqrt{A^2 + B^2}$ in general equation of line, if any? typo Oct 6 comment How to tell if multivariable function is odd? You just do. It's something you get used to after a while. After all, it's usually pretty easy to tell at a glance whether a function is odd. Oct 5 comment Let $f,g$ be two distinct functions from $[0,1]$ to $(0, +\infty)$ such that $\int_{0}^{1} g = \int_{0}^{1} f$. Are those powers or derivatives? Oct 1 revised Is the function $f(x)= {\sin x \over x}$ uniformly continuous over $\mathbb{R}$? added 11 characters in body Oct 1 awarded Benefactor Oct 1 accepted Why do we think of a vector as being the same as a differential operator? Sep 30 comment Why do we think of a vector as being the same as a differential operator? I think I like your answer the most, but I'll wait a bit longer just in case another one pops up. Thanks! Sep 29 comment Why do we think of a vector as being the same as a differential operator? Why is it the only sensible definition? If I have a point $p \in M$ and an open set $U \ni p$ with local coordinates $\phi: U \to \mathbb{R}^n$, then I can choose (for example) the standard basis of $\mathbb{R}^n$, and if I want to use another coordinate system, the vectors transform as dictated by the Jacobian, so my basis is well-defined regardless of the coordinates. Isn't this right? Sep 28 comment is it true that $\det(I+A)>0$ , if $\det(A)>0$? +1 This is the simplest example, I think. Sep 26 comment How to show that the is a $1-1$ correspondence between real numbers and the set of points of a line in the Euclidean plane? I think the question is about the relationship between $\mathbb{R}$ as a set of numbers and the geometric notion of a line, but I could be wrong. Sep 26 revised Surprising identities / equations added 29 characters in body Sep 26 awarded Promoter Sep 25 comment Why do we think of a vector as being the same as a differential operator? @GeorgesElencwajg: If you think that's the answer, then post it as so. But I still wonder: if there's no reason to make no distinction, why does the author make no distinction? Sep 23 asked Why do we think of a vector as being the same as a differential operator? Sep 22 comment Simplify the expression. Isn't this needlessly complicated? Why not just substract exponents at the second equality, if you're going to do it later anyway? Sep 21 comment Integrating $\sec^2 x$ from first principles Why would you not know that? It's not magic, it's very easy to derive. Sep 21 comment lim calculus problem with infinity @vilbur: $\frac{n+5-2}{n+5} = \frac{(n+5)-2}{n+5} = \frac{n+5}{n+5} - \frac{2}{n+5} = 1-\frac2{n+5}$. Sep 21 comment lim calculus problem with infinity Also, the nth-root of n goes to $1$. If you don't believe me, take the logarithm of the expression. Sep 21 comment lim calculus problem with infinity The fraction goes to $1$ but the exponent goes to $\infty$; this doesn't go to $1$ but rather is an indeterminate case, as evidenced by the well known fact that $(1+\frac1{n})^n \to e$.