@ᴇʏᴇs This occurred to me randomly: Physicists call the energy-momentum tensor in string theory and conformal field theory holomorphic. A pedantic mathematician would insist that it is actually meromorphic.
I've seen weird downvoting, but what's up with my answer and the deleted answer on this question? We both got five downvotes for answers that, while not perfect, were not wrong. math.stackexchange.com/questions/1208336/…
@ThomasAndrews Didn't vote, but I agree your answer is more complex than is needed, and many of the downvotes probably come from the 'don't answer a PSQ' mentality
But the other answer is the simpler approach (which is why I gave the complicated - some people don't know why $x^ax^b=x^{a+b}$ when $a,b$ rational. And that other answer got $5$ downvotes. @Committingtoachallenge
And OP selected my answer. :) Maybe it somehow got promoted to the front of the stackexchange site, so we got lots of outsiders/irregulars visiting.
Did you get a badge for strongly downvoted accepted answer?
Also, your answer Thomas is horrible and extremely complicated for a simple thing. If 2 donwvotes were allowed, I would definitely downvote your answer twice. – Anonaki
@ThomasA if you edit it(so people can change their votes) I am sure some people will change them, given that yours was the one accepted
Yeah, I saw that comment. I can't help it that he doesn't understand. :) I'm happy to have a selected answer with downvotes. And, since OP selected it, it's hard to say it didn't help OP. Anyway, I've seen answerslike this downvoted, but not seven times. And I don't know why the question is upvoted, either - it's trivial algebra. I don't care about the points, I just feel like there is something odd happening. Maybe an external link to the question.
Basically, the decimal expansion of a real number shows that you can stop at $n$ digits and get a "rational" number arbitrarily close to any real. If $a,b$ irrational, find a rational number with $\epsilon$ of $(a+b)/2$, where $\epsilon<|b-a|/2$. @Committingtoachallenge
@JasperLoy I would have preferred him to just say "Don't be discouraged, we can help you" and leave out the other BS that he has no place in mentioning on your first visit to him. It makes me wonder if they are actually taught to say that?
Please be gentle as I do not have any degree in maths.
By using a compass/straighedge method to construct Metatron's cube, a regular dodecahedron can be inferred from intersecting points. I'm looking for the ratio between the lengths of the edges (blue) of the dodecahedron and the radius of the ...
@infinitesimalsimplicio If he was overly positive, they are meant to do that since it has been shown to greatly improve their rate of success on depression/anxiety, since it increases your suggestiveness
@ThomasAndrews First I have heard of it
Was that why he only considered the case when $x_0\in \Bbb Q, x_1\in \Bbb I$ and $x_0 \in \Bbb I, x_1\in \Bbb Q$?
Because there are infinitely many of the other set between each element
the search for an "impossible $\epsilon$ to satisfy, is going to depend on finding points near each other on the real line, but whose images are far apart.
Unfortunately, it only tells you one exists, it doesn't help with really finding one.
"Suppose a partially ordered set P has the property that every chain (i.e. totally ordered subset) has an upper bound in P. Then the set P contains at least one maximal element."
The idea is this @Committingtoachallenge: you know that for a given $x$, the rationals near $x$ map near $x$, and the irrationals map near $-x$. So choose $\epsilon = |x|$.
In the second paragraph of this note, Sarnak mentions that the projection of $SL_n(Z)$ to $SL_n(Z/qZ)$ is surjective. Isn't this elementary? Doesn't it just follow from $Z \to Z/nZ$ being surjective?
Hmm, I am not really sure (never really worked with these things) honestly, I am guessing it is not necessarily obvious it that a reduction would preserve the determinants properties.
I am not sure if I am confirming, like I said I have never really messed with these things, but I wouldn't be surprised if that was the reason. Maybe I will try to prove it in a bit, or you can keep me informed if you confirm.
@Committingtoachallenge but he wasn't being overly positive. What he said was "don't kill yourselve, we can help you" and I strongly object to him saying "don't kill yourself" on the very first visit. Since he is, after all only a stranger at this point; and has absolutely no idea of how bad the situation may be. In other words, he has already set back any therapist by announcing his "opinion."
@JasperLoy I would have preferred him to just say "Don't be discouraged, we can help you" and leave out the other BS that he has no place in mentioning on your first visit to him. It makes me wonder if they are actually taught to say that?
I have shown that $$\lim_{x \rightarrow 0} \frac{\sin 2x-2x}{x^3}=-\frac{4}{3}$$
How could we check whether the limit $$\lim_{(x, y) \rightarrow (0, 0)} \frac{\sin 2x-2x+y}{x^3+y}$$ exits or not?? @DavidWheeler @ThomasAndrews @robjohn
No. For example, if $G$ is any non-cyclic group, and $S$ is a set of generators, no $g\in S$ is a generator. @infinitesimalsimplicio The "of generators" does not match the normal pattern - it is actually a property of the set as a whole, not of the elements.
@DavidWheeler @Bib Ah, yah. I guess it is that its not necessarily non-trivial to say that every matrix with det 1 in the reduction comes from a matrix with determinant 1 without the chinese remainder theorem.
(which now that I think about it is the obvious application of the chinese remainder theorem in the problem)
I've been thinking about the growth of the site recently, and about the problem of duplication. On a whim, I looked at the number of posts containing the "euclidean algorithm", and there are over 1500
how many of these posts are abstract duplicates of each other? And is that a problem? I've been thinking of these questions
one might argue that having a central euclidean algorithm post would be enough. But that's essentially what a textbook provides, and that's usually what drives people here
@mixedmath Maybe, I am guessing there are less than 100 "gems", and I am sure those would be easy enough to find based on votes and the people who frequent that tag.
I wouldn't be against it (I can think of at least one person who would complain and threaten to leave math.se though)
I am sure similar things can be done with many tags, or key words, not just euclidean algorithm. For example there are over 500 questions with product rule or chain rule in just the title, and I am sure there are many other questions that are asking about one of those rules without putting them in the title. @mixedmath
@infinitesimalsimplicio This might be one of those things where concerted effort in the short term will save a lot of heartache in the long run. Maybe.
I've previously played with the thought of deliberately "curating" some of my favorite tags so that the quality and searchability remains high
a key aspect that helps searching is having question titles be meaningful, for instance. A quick glance at the front page shows that this is actually something to ask for
I still learn a lot from reading good number-theory posts, too. But it's also a huge time sink, so I only do it occasionally
I think we are all a little guilty of that. I think it comes form the title being the first thing written a lot of the time, so we haven't consciously made the question as specific as we could (and we should) at that point.
It's very interesting, the right one seems to fit better, but after a 10 degree rotation of the dodecahedron, the vertices seem to line up exactly with half of the star tetrahedron
Please be gentle as I do not have any degree in maths.
By using a compass/straighedge method to construct Metatron's cube, a regular dodecahedron can be inferred from intersecting points. I'm looking for the ratio between the lengths of the edges (blue) of the dodecahedron and the radius of the ...
well can somebody answer this question if a set A contains 15 elements and set B contains 25 elements then how many elements does the symmetric difference of A and B contain
the question again is: if a and b are two sets such that the elements in a are 15 and the elements in b are 25 the number of elements in the range of a and b is:
I think it is trying to get you to see how many different ways are their for a "generic" symmetric difference to occur between a set $A$ with 15 elements and a set $B$ with 25 elements. $A$ and $B$ can agree on 0 elements, or they can agree on 1 element, or 2,...., or 15 elements. Which is 16 altogether. This interpretations is still a stretch of the imagination so I would get clarification from your prof. @SayanChattopadhyay
I just explained, there are only 16 ways for the symmetric differnce to come out since the set $A$ has 15 elements, so $A$ can agree on 0,1,2,...,15 elements of $B$ which has symmetric differences of distinct cardinality. But like I said I think you really should get this cleared up with your prof because the quesiton still doesn't make sense
Which is uniquely defined by how many elements they have in common...(the symmetric difference as usually defined is the set of elements in A or B but not both) What is the definition of symmetric difference in your class?
Seek help: http://math.stackexchange.com/questions/1208424/l-cdot-m-pi-rsl-otimes-m-then-f-i-cdot-f-j-cdot-f-k-cdot-f-l anyone familiar with multi-linear functions, exterior product, could spare a look?
@maja: Trying can't hurt, but I'd search for similar questions before. If it's common in the US to allow calculators on calc exams, I'm sure someone else has asked this before.
@ys wong the website seems well structured, but I do have understood our topics until now (still at the integrals part of the course). anyways, I put it in my studying resources, thanks
@DiscipleofBarney Well my votes for the week are at 240, so either I happened to exceed the 40 a day(via deletions) by exactly 40, or the week starts on sunday
(and I have forgotten to vote equally to my exceeding the cap)
@infinitesimalsimplicio Are you at math uni? Or doing some math texts? I don't remember if you are asking this(admittedly changing names constantly will desync my memories from you)
Ah, makes sense. Notice you have a lot of down votes? Do you spend those on recent questions or old questions (to get Community to delete them), or some combo? @Committingtoachallenge
@Committingtoachallenge Did you think about groups of order $p^2$ anymore after our discussion on the linear algebra room? You should finish it if you have time.
not quite. it's a way to draw the subgroup structure of a group. not particularly very important, but you can get a very good geometric picture of quotient groups from it.
