Recent content by olliemath

OK, conserving probabilities is clearly necessary but I'm not sure exactly what you mean.. if (V_t) is a semigroup of isometries and \psi_t=V_t\psi_0 we obtain <\psi_t|\varphi_t>=<\psi_0|\varphi_0>, which is what I understand by conservation of probability The time aspect is a good point.. I...

I think this is the right forum for this.. are there any physical reasons to assume the evolution of a quantum system is given by a group of unitaries rather than a semigroup of isometries (or, if you're in the Heisenberg picture, group of automorphisms rather than semigroup of endomorphisms)...

I always find it easier to work with a specific example and generalise.. e.g. take the interval (0,1) on the real line with standard metric - what are it's features, why is it not complete? Why is (-infinity,infinity) complete when the two sets are topologicaly the same?

This is not important, but it's been bugging me for a while. I'm struggling to see how the locally constant sheaves of vector spaces on X give rise to representations of the fundamental group of X. The approach I've been thinking of is the following. Given a locally constant sheaf F on X...

According to my calculations (proof) it's not possible.. Try proving this..

I thought p-adics only had uses in number theory, shows how ignorant I am! They're basically just a different way of extending the integers (or rationals), by adding extra `numbers'.. The p-adic integers are an extension of the usual set of integers. If you've done any modular arithmetic you'll...

Interesting.. it looks like the sort of question that might've been studied by victorian mathematicians.. like you say it's quite easy to construct even monotonically increasing functions for which the patturn is broken, so I don't think there'll be a general result. If we call f(x)...

If you mean proffessional mathematicians as in researchers then geometers.. in various areas of differential, algebraic, Riemannian, noncommutative geometry etc. or mathematical phycisists involved in general relativity and string theory, or differential topologists.. there might be other people...

Clearly H is a group and it's a topological space. It need not be an open set on the topology on G (if it's a subspace in the sense I think you mean - a subset with the subspace topology). What you need to show is that the restrictions of the multiplication and inverse maps to H are still...

Would it not be much easier to treat it like a Fourier series? :-) (Mind you, I haven't tried so I don't know) Anywho I got a little confused when reading because you went from talking about sums of \sin(n\pi x/L) terms to \sin(n\pi/L), i.e. the value of the whole thing at 1. Anyway, assuming...

I like the classical form (I think because I have the memory "wow, maths can be beautiful" associated to it, rather than its intrinsic genius) but I can see why you like the more topological version.

Well it isn't a, it's f(a). This idea is used (without mention) again and again throughout mathematics. Whenever you find the roots a,b of a quadratic equation you tend to write it in the form (X-a)(X-b). So a question to ask yourself is: how do you know this is always possible? What about...

If you take category theory as the standard then since nothing is more like category theory than category theory everything else falls a bit short. :smile: I suppose I'd put logic up there because while you use e.g. set theory and category theory to study mathematical structures, logic can be...

Your formula should work perfectly well, you just need a little thought to work out what your a and b should be in this case. What is the probability that the plane does not return in 20 minutes? If it returns in e.g 30 minutes then clearly it doesn't return in 10 minutes, so P(30 mins and not...

Continuity in the way I first heard it: A funtion f:A\subseteq\mathbb{R}\rightarrow\mathbb{R} is continuous if, for each x\in A and each \varepsilon>0, we can find some \delta>0 such that |f(x)-f(y)|<\epsilon whenever |x-y|<\delta. I know a lot of people tend not to like it when they first...