@KyleKanos I am not assuming you don't know anything about particle or Lagrangian methods in my comments, but I am assuming the OP doesn't and just wanted to point out that the Lagrangian way of looking at things is a possible treatment as well
Just to clarify my comment some without leaving more comments :)
@dmckee I've actually just found myself deleting my own comments and tapping out of a discussing entirely if people get argumentative. Or just ignoring the bait (which is probably the thread you are referring to, which I missed a lot of because I got there seconds after it was nuked)
Although I guess I may have started that whole problem... @Jim 's first response was really good though. I wanted to say the same but was adopting my "ignore the bait" policy.
@tpg2114 I had a couple of recent one and a few further back in mind, but I didn't notice any you were involved it. Nor do I want to call anyone out, because all the regulars are good at staying in bounds. It's just that the act of engagement can bring less regular users to a peak of xkcdesque need to explain why they are right.
It's long overdue that I make this post revisiting our policy on "check-my-work" questions. These are questions, often (but not necessarily) homework-like, that present a complete mathematical or logical derivation and ask whether it's correct.
Historically our homework policy has rendered check...
@tpg2114 it's a lot of "hey other mods, look at the flag on [post]" and "is this worth deleting?" and "FYI I'll be out of town next week." Much lower activity than this room.
honestly, if you want entertainment you'd be better off looking at the mod flag queue :-P
@tpg2114 thanks for the compliment. I usually take a different policy regarding internet arguments than most of you it seems. I just argue for the sake of arguing. It's not really about what I argue, more about how I argue it. Like a game, I mostly don't care about who's right, I'll even argue with people who say I'm right. But I'll argue back because it's fun to try to make rational and logical points out of a given stance. That's why I responded by defending your comment, it was a good move.
@ACuriousMind oh, no, it has to be since something converges to a point x in the topological sense if it's inside all the open sets containing x. In the case of the trivial topology, everything converges to everything and therefore it's the weakest one, I guess
@Jim I used to do the same, but I realized on the internet there's a never-ending source of people like you on the other side. And so it will never end and just get annoying
So I keep it that strategy to my in-person life only now
@Danu I think you are right there. Weakest topologies (in a categorial sense) are also often those induced by requiring that some maps into a space be continuous - think of, e.g., the product topology or quotient topologies.
Haha...that's all too common sadly. I seem to recall that a sequence of points $x_i$ in a topological space $X$ converges to $x \in X$ if, for every open neighbourhood $U$ of $x$, there is an $N \in \mathbb{N}$ such that $x_n \in U$ for every $n > N$.
Note that, for general topologies, convergence in this sense is not unique - there can be several limits, or a limit might be "missing", i.e. you think it should be there, but it isn't
The epsilon-delta definition is just a more confusing way to talk about open neightbourhoods ;)
One can have fun (of the mathy kind ;) ) with this kind of convergence - algebraists call the operation of "adding" the missing limits completion, and it is a functor with some applications
@Danu I hate it, but perhaps only because of the lost hours trying to find the right inequality to get these frigging epsilon coming out right for analysis assignments :D
Right... I could see that. Also, does it matter whehter you use neighborhoods of X or open sets containing X in your definition of convergence? No, right?
Deļ¬nition: A set N is called a neighborhood of a point x e S, a topological space, if there exists an open set U with x e U c N.
lol my PDF reader OCR'd \in as e and \subset as c
(that was a copy-paste from my R&S textbook)
...and a little bit later: We emphasize that neighborhoods need not be open. In a metric space, the closed balls of radius greater than zero are a neighborhood base.
@Danu There's a TeX/PDF feature where you can declare the text/Unicode that should be copied from a formula - so it may be that it was not your reader, but a very thorough TeXer ;)
There's probably an "open" missing in front of neighbourhood in the convergence definition then, but also probably it does not matter.
My "basic topology" dealing with these things - neighbourhoods, metric spaces, convergence - is quite weak though, I'm mostly versed in algebraic topology. I'll take chain complexes over epsilons every day ;)
@Danu That fear is best to be fought! We are always lower than someone and higher than someone else. But the community is friendly on this phys.SE and I think it should be on math.SE as well.
@ACuriousMind There are always two sides competing, the nascissist side of one's nature and the paranoid side of nature. Results cover the full spectrum [0;1]. So I think there exists such someone, though maybe not many such people.
Either way, Is mind reading possible? is a title that seems made for the Hot Network list.
Some other day, there was a What use are friends, anyway? question there. It was referring to a question on Arqade about some obscure casual online game where you could add "friends". Needless to say, I was disappointed.
I am currently doing research in a subset of the field of gravitational lensing called weak lensing. I am simulating blended galaxy profiles and creating an algorithm to extract the true parameters I created my image with. I am then assessing the accuracy of my algorithm.
Since this is my first...
I am currently doing research in a subset of the field of gravitational lensing called weak lensing. I am simulating blended galaxy profiles and creating an algorithm to extract the true parameters I created my image with. I am then assessing the accuracy of my algorithm.
Since this is my first...
