I have no idea yet what you're talking about, @Semiclassic. Classically, incidence refers to points contained in lines, or lines contained in planes, etc. What are you talking about?
@iwriteonbananas I forget all this framing stuff. The point, informally, is that the orientation of the boundary of M x I is different on the two sides.
That's the only way I can write. The big goal, obviously, is the paper. Slmetimes the small goals are "figure out what the norm map is", sometimes "write down the basic transversality argument", sometimes "get all that horrible notation into the page".
Yeah, I guess I shouldn't hope to go outside of that. I'd presumably preserve the crossing structure if I did a projective transformation, but they'd no longer be lines.
Well, projective transformations won't stay in the Euclidean plane, @Semiclassic. If you enlarge my universe to $\Bbb P^2$, then, of course, projective transformations is what we want.
In any case, I don't have any reason to hope that what's being claimed in the paper to hold if I replace lines with circles. So affine linear group seems to be all that one can hope for.
But, as in the case of complex LFTs, some points (indeed a line) will map to infinity, so our universe isn't preserved if our universe is the Euclidean plane.
DogAteMy is working through your book, and Alessandro's going to do differential topology after 13th (I think?) so you'll have a lot on your plate soon
There's the oral part of the numerical analysis exam on the 20th @Balarka. But I'm starting to feel prepared enough, I was thinking about reading some G&P tonight. (Also because I finished doing all of the exams from previous years so I don't know what more to do now)
@Ted I might talk about the "homotopy principle" (not Gromov's) - if you can do something for an arbitrary choice, and the something you can do is well-defined up to homotopy, and your choices are connected by homotopy, you have an invariant.
Maybe I'll talk about the "generalized degree" of a map between arbitrary closed smooth manifolds - a homology class in $H_{\dim M - \dim N}$ - and why it's worthless.
@Balarka: When you review forms and learn Frobenius, we can do cool stuff (including why $K=0$ gives a surface isometric to $\Bbb R^2$, assuming simple connectivity).
Actually, that's easy for surfaces, no Frobenius needed. But we can do higher-dimensional interesting stuff.
@TedShifrin they helped me on the first course this year about linear algebra =p but i will ofcouse watch them all when those things cames up or on summer just to learn more
If you're a math major, @Kasmir, thinking of the derivative as a linear map will be quite helpful. Somehow I thought you were more engineering, so I discouraged you.
When I taught the course, @Alessandro, I stated all the transversality theorems and used them, and then proved them a month or so later. Just so students would see the beauty and power of using them first.
One way to understand it is via Euler-Maclaurin. In that case, you'd expect to get terms like $n^{-k}$. But the coefficients of those terms essentially measure to what extent the function (or its higher derivatives) must 'jump' in going from one endpoint to the other.
But really, I agree breaks are good. But if you want to do something, you need to make an active effort to do it. And when you want to not do something, you need to make an active effort not to.
two people, Alice and Bob move on a line. Alice starts at Y at t=1, and reaches X at t=2. Bob starts at X at t=0, and reaches Y at t=3. Now, how can we reason that they meet each other on the way?
and then, construct a distance function between both, and show that it is positive at the beginning and "negative" at the end, but that makes no sense i guess
Hello, i have an excersice for my school about showing a problem belongs to NP-Complete class. Would it be possible to write the problem and give me some hints if you can, at least to say to me if i am at the right direction? Thanks.
Okay here is the problem. Given a undirected graph G(V,E) and a subset of the edges, named F (F subset of E), is there a simple cycle at G that comes from every edge of F? Show that this problem belongs to NP Complete
The reason i am not asking it as a question at the mainsite is because i am sure i would be downvoted many times. My knowdledges are verry little at computation theory and my professor doesn't explain anything. I am hardly trying to understand them, i just searching all the time and i am not sure where i should start. I am sure it would be something close to CLIQUE problem and HAMILTONIAN cycle.
Because i am actually looking for a big part of the solution, as i said i don't know even where to start, so i can't provide what i have done so far. That's why. Maybe i am wrong.
if i have a 2d space filled with interactionless dust moving randomly from infinity, and i put a polygon in the space to catch the dust, the amount of dust i catch should be equal to the surface area of its convex hull, right?
Because the timeframe of typing the message is around the timeframe of the time stated; it becomes very important at what moment those $0.2$ seconds started
Depends on the something, perhaps. For instance, if I were to claim that 27 is prime, I can easily be disproven by noting that 3|27. But no such counterexample is possible for 29, so 29 is prime.
But I'm not sure that's quite the same as what you said.
Let's say I have a property $P$ I claim true for all natural. If my statement is wrong, you can prove it's wrong by giving $n\in \Bbb N$ such that we don't have $P(n)$ after trying a few. However does that mean you can demonstrate the property if it is true ?
Third line of wikipedia's article on Gödel's incompleteness theorem states that "The first incompleteness theorem states that no consistent system of axioms whose theorems can be listed by an effective procedure (i.e., an algorithm) is capable of proving all truths about the arithmetic of the natural numbers."
@Kirill: Note that the sum starts at $k=2$ so the value at $z=0$ is $0$. And the power series defines a continuous function (in fact, infinitely differentiable function).
I don't know what you're trying to do, @Kirill. But it's a well-known fact about power series: They are infinitely differentiable on any open interval where they make sense (i.e., converge).
But nobody on that working group has a strong mathematical background, so I'm wondering if I should send in a poster filled with Mathsgen nonsense to troll them...
@Astyx yes, it is. I split 2 and $z$ from it and have $1 + \texttt{the series above}$. I have to show that $\frac{e^z -1}{z}$ converges to 0 for $z \to 0$. Tha is why I am asking myself - is that ok, if I say that the series converges to 0, or should I prove it additionally?
@SteamyRoot lol! But I must say this is really well done. I guess for someone with no maths background this is indistinguishable from a real maths paper. That you can actually get published with it is another story...
I'm saying that if prove the limit as $z\to 0$ for $\sum_{k=1}^\infty \frac{z^{k-1}}{k!}=\frac{e^z-1}{z}$, then you also know it for $\sum_{k=2}^\infty \frac{z^{k-1}}{k!}$ (it only differs by 1). So if it proves simpler to do the series starting from k=1, then you can do that.
@Semiclassical I have to show that it is 1, as @Astyx wrote before. I decided to split 1 and am trying to prove that the series converges to 0. My original question was if I should?
can you devide a circle's circomference into equal parts, which are alternatingly painted black/white, such that there exist antipodal points that share the same color?
