Is there an elementary expression for extracting polynomial coefficients? I would have guessed no, since I've never seen monomials used as an orthonormal basis...
I don't want to poop in the party, but if anyone wants to answer an elementary, high-school level math question, I'm looking for advice. Anyone have 5 seconds?
i spent two months in the hospital under the care of two great nurses who (along with their husbands) were huge Raiders fans (their husbands were from Oakland originally and used to be in the Black Hole at every home game until moving to NY). Those months included January 2001....
they were some the gentlest people I've ever met, and really took care of me during my recovery. So, I always think of them when I see a Raiders game on TV
I think Al Davis deserves a lot of credit for the successes of that organisation
I spend way too long on the most basic, pathetic problems, then someone comes along, or I read a line somewhere, and it's revealed to me as being as lowly as it is. And without having read or heard whatever it was, I'd be stuck in this disgusting pit of not understanding. It really makes me wonder about my capabilities.
@robjohn, I changed my question, adding in what I've just learned from you. Would you mind taking a look to see if my work is correct? math.stackexchange.com/questions/96789/…
Is there a way to stop people editing my questions? Every time I return to my own questions, someone is in the process of formatting how they like it and it's thoroughly irritating.
Would you say the derivative of f(g(x)) was f '(g(x)) or (f(g(x)))' ?
@Skullpatrol If it's used as $X \ni x$ then it's fine with me and a reasonable usage. On the other hand using $\ni$ in the sense of "such that" is thoroughly bad and completely unnecessary.
@Srivatsan To be honest I don't understand the whole unnecessary braces thing some people here have going. Why bother? There's absolutely no need to remove them, it doesn't make any sense to me.
I appreciate the effort in retagging and general clean-up, though.
@Srivatsan Yes, but it's highly nontrivial and due to Brouwer. It's called invariance of domain: a continuous injection from $U \subset \mathbb{R}^n$ to $\mathbb{R}^n$ is open.
In general, under what broad conditions does such a thing hold? I.e., every continuous bijection $X \to X$ is a homeomorphism. I think it is true if $X$ is compact.
@DylanMoreland yes, every basic algebraic topology text worth the name proves it. There are also proofs that avoid homological machinery (as did Brouwer's original one). I think there's one direct approach in Dieudonné's treatise of analysis.
@Srivatsan as I said: whatever assumptions you like. Just show that $f$ maps closed sets to closed sets (because closed subspaces are compact and mapped to compact sets which in turn are closed).
@Srivatsan That's basically the gist of it. I would definitely not appreciate it if someone removed my superfluous braces... I understand that you re-tagged and made some other minor things, which is perfectly fine with me, but again: what is the point of removing unnecessary braces? I almost always use braces out of habit, why should I bother to add them to other posts so others do that as well? I basically can't read code of the form $\frac1x$ and I find that distinctly ugly.
@Srivatsan $X$ compact and $Y$ Hausdorff is what's needed.
@tb Does "contains as an element" = backwards epsilon, and "an element contained within" = forwards epsilon show that the "epsilon relation" is a invertable relationship?
@Srivatsan: Look at this here. In my opinion the source is a horrible mess. But obviously the OP has his own quirks of (bad IMO) taste, so I just leave it... Even though I'm very tempted to adjust the misplaced tildas and to remove about one hundred spacing thingies.
Obviously the second one is the typographically acceptable one, while semantically the first one is correct.
The first one is very bad typographically.
@Skullpatrol No, it does not mean that. At most one of the relationships $A \in B$ or $B \in A$ can hold. So if $A \in B$ holds and you want to switch the places of $A$ and $B$ you need to write something else and $B \ni A$ seems the logical thing to do.
+1ed your comment don't understand Mariano's either.
@Skullpatrol Here's an example where I sometimes use it: in topology you often have to say: "given a point $x \in X$, let $U$ be an open set containing $x$." If I need several such instances I might write: "Given $x,y,z \in X$ choose pairwise disjoint open sets $U \ni x$, $V \ni y$ and $W \ni z$" or something to that effect.
The question is extremely clear conceptually (quite surprising :-)): the OP clearly understands the two interpretations and asks which one is standard.
Hah, yeah. I took a recipe from my mom and just cut all the amounts in half. But I put regular amount of sugar so I had to use a spoon to take out half a cup of sugar from the top of the pile... I probably missed a bit.
@tb In mathematics, each negative number can be said to be the opposite of (or paired with) each positive number. Thus they are opposites of each other and therefore belong to each other as opposites, true?
@Srivatsan Yes. This was Willie's comment to that question: _I don't see the problem: deep below the surface they are all the same thing. I am however in favour of a tag wiki that briefly mentions inversion as an abstract concept and asks the user to specify the regime where the idea is used in the question. _
@MartinSleziak Exactly. If you notice the meta post, I suggest removing inversion, whereas JM suggests doing something with [inverse], but he explicitly says he is not suggesting deleting the tag.
I'm not really sure, but I have not made any [inverse] edits recently. We have only removed [inversion], and moved many of them to [inversive-geometry] -- that is good.
@Skullpatrol I think they fall under algebra-precalculus fine. If we tried to create tags tailored to school system of some country, probably users from different countries with different school would not agree.
Just check how different meaning can real analysis have: see this conversation.
@Skullpatrol Perhaps we are dividing things too finely here. I think the difference between High School Algebra and College Algebra is clear; they are two different subjects. Perhaps I am missing something here.
@tb I think that the best thing would be to keep the original version of the post and then add an LaTeXed version. And ask OP to confirm, whether it is what he meant. (And to learn using math here.)
Is there a volunteer to do this? (It would be waste of the time if several people would try to edit it at once.)
Anyone tell me: should I cut this answer in two pieces? The part up to "At the moment" is basically my clear yes as an answer, the rest are some thoughts for considerations to be made.
@robjohn I agree, the difference between High School Algebra and College Algebra is clear; they are two different subjects, but algebra-precalculus is a separate tag and I am only suggesting an algebra-high-school tag?
@robjohn I only tried to rewrite formulas. I was not able to decipher anything from ASCII-art. If you guys are able to read mathematics in ASCII, I sincerely admire you. I am able to read some short formula, but not such a long post.
If I had to choose whether read some math in ASCII art or in Russian language, I would go for Russian. Despite my problems with reading Cyrillic.
But the OP started to edit his answer after my modification already. Even if the only useful thing is going to be that he learns basics of math markup, it was worth the trouble.
@robjohn Well at sci.math you don't have much choice. (I wish google groups added an option to use mathjax; it's about time. Not for sci.math; but in some google groups I used to communicate with my students or my colleagues, it would be helpful.)
@Srivatsan Yes, they are two separate but reciprocally related symbols, in that if two things are paired with each other in such a way that they belong to each other, these two symbols become interchangeable.
@MartinSleziak Two brothers belong to each other as bothers. One brother has a brother and the other brother has a brother, they belong to each other as brothers.
@robjohn Can you see that the forward or reverse "epsilon" can be used to express "belonging to" or "possessing" for things that are paired with each other?
@tb You're welcome. Just to confirm - poster is pinged even whet it's CW right? (So you get a ping from my comment even though I did not use @t.b. there.)
