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 2h comment Chain Rule For Limits @A.G. Note that the question says that $p = \infty$. 1d awarded Teacher 1d awarded Yearling 2d answered Evaluate $\iint dy\,dx;\frac{\pi}{4}\leq\theta \leq\frac{3\pi}{4};0\leq r\leq2$ Jul23 comment About the solution of $2^x-x^x=0$ $0^0$ is very "dangerous" as its definition may depend on approach. As Argon mentioned, the limit of $x^x$ is $1$ (even from a negative side, the imaginary part converges to $0$). However, if you generalise to the function $f: \mathbb{R}^+ \times \mathbb{R}^+ \to \mathbb{R}: (x,y) \mapsto x^y$ you may get different results depending on the order of your limits (you will get 1 or 0 depending on $x$ or $y$ first). Jul23 comment Equation for position, moving with a value J of the third derivative of position. Are you asking about the physics behind this, or the mathematics? Mathematically you just integrate $\frac{d^3x}{dt^3} = J$ three times with respect to $t$. Jul21 comment Connected Lie group is second countable? I see, I'll see if I can come up with something using that. Thank you for your help. I'm indeed Belgian - I had a look at your webpage and noticed some familiar authors among your publications, which is why I asked. Jul21 accepted Connected Lie group is second countable? Jul21 comment Connected Lie group is second countable? I'll have to take your word for it... Unfortunately I haven't had time yet to look into Lie algebras, and the text I'm using simply defines a Lie group as a group that is also a differential manifold (with the conditions on the multiplication and inverse map, of course) - but there is no mention of Lie algebras anywhere. Do you think there is a way to prove it circumventing the need for the Lie algebra? An another (and more personal note), if you don't mind me asking: am I correct in assuming that you will be the promotor of a certain Belgian Erasmus student next term? Jul21 comment Connected Lie group is second countable? Finite-dimensional Jul21 comment Connected Lie group is second countable? Ah, you are right. Thank you! Since I still don't know how to prove it for a Lie group, though, I've taken the liberty of changing the question. Jul21 revised Connected Lie group is second countable? added 61 characters in body; edited title Jul21 asked Connected Lie group is second countable? Jul20 accepted Set of discrete orbits under subgroup of $Isom(\mathbb{E}^n)$ is clopen Jul20 revised Set of discrete orbits under subgroup of $Isom(\mathbb{E}^n)$ is clopen added 72 characters in body Jul20 comment Set of discrete orbits under subgroup of $Isom(\mathbb{E}^n)$ is clopen @studiosus Ah, you're right of course. $O(n) \cdot 0 = {0}$ which is discrete, but for any $x \neq 0$ the orbit is the sphere of radius $\|x\|$, which is clearly not discrete. I should've been more critical of the question itself, I guess. If you post this as an answer I'll accept it, otherwise I'll just delete the question I guess. Also going to update the question to reference the source. Jul20 asked Set of discrete orbits under subgroup of $Isom(\mathbb{E}^n)$ is clopen Jun13 asked Proof of Hopf's theorem using Liouville May16 comment Euclidean distance on R and Q To solve iii), including rays in the definition of open intervals is unnecessary. A ray of one of those forms can easily be written as a countable union of open intervals, e.g. $(a,\infty) = (a,a+2) \cup (a+1,a+3) \cup ....$ May16 awarded Informed