Ya to me this seems more useful as an invariant either of symplectic manifolds or of submanifolds of contact manifolds (Leg, and transverse). I don't know how to say many things about contact strs. themselves.
@Semiclassical Not sure if they are actually called Catalan polynomials. That are similar to Fibonacci polynomials, though they satisfy a slightly different recurrence.
@BalarkaSen One has to show there is a countable open cover with certain properties. For example, one can show there is a countable open cover such that $U,V$ and $U\cap V$ are simply connected for all $U,V$.
I mean if the co-domain is a group of integers under addition and the domain is a group of non-zero rationals under multiplication will the floor function be surjective?
Oh, anyways: Find the number of regia that space 3D space is divided in by $N$ planes in general position
I solved it using the easier problem of the number of regia that a 2D plane is divided into by $N$ lines in general position, has anybody got other ideas?
What is the meaning of humbleness in mathematics? Loving and respecting mathematics also means to get very top results in it, or tying to get them (at least).
Norms on a vector space $V$ are special kind of maps $V \to \Bbb R$, thus it doesn't make sense to ask if they take infinite values. In this case, the sup norm is actually a norm only when it is actually a real number. I.e., on bounded sequences, it's a norm.
Why are norms maps to $\Bbb R$ and not to $\Bbb R \cup \{\pm \infty\}$? Because intuitively they measure how "long" a vector is on your vector space. Setting length to be infinity for some vectors messes the intuition up!
@Mambo Pride is also relative. I think, if considering the negative conotation of pride, that it might be sometimes useful. If you ask me, I think its very hard to be pride in front of a nice, respectful person.
