Recent content by iopmar06

Thanks for your replies. I can see where I should be going with a) but I'm still working on it. a) Consider the metric space (R,d) where d is the euclidean metric d(x,y)=|x-y|. Note that if (X,d) is a metric space then a subset Y of X is called closed if for every sequence (y(n)) of elements...

Homework Statement a) Let U be a closed subset of the reals with an upper bound. You know that U has a supremum, say z. Prove that z is an element of U. b) Suppose U is a closed subset of the real numbers with an upper and lower bound. Prove that U has a maximum and minimum.The Attempt at a...

Why not?

Would the following argument be sufficient? If two sets A and B are countable then there are bijections f: A \rightarrow N and g: B \rightarrow N. Define a map p: (A U B) -> N by p(n) = f(n) if n is in A p(n) = g(n) if n is in B\A If you show that p is a bijection then (A U B) is equivalent...

The "a" in my answer should be a "b". I didn't look at the diagram properly.

To be honest I am only an undergraduate so not much. Just basic topology and algebra.

My course is using Shaw's Complex Analysis with Mathematica. It's a pretty good even for a non-Mathematica based course. Just avoid anything with "engineering" in the title.

Lecture notes, assignments and other useful materials for a unit on complex analysis that I am taking this semester are available from: http://www.maths.uwa.edu.au/~keady/Teaching/3M2/index.html The lecture notes were originally written in the 80's but they have been updated and are very...

Yeah I'm just in the habit of using v for velocity. Anyway, thanks a lot for all your help.

That completely slipped my mind, thanks for pointing it out. The cylinder is not slipping so v = \omega r Substituting this into the inequality gives v^2 > 2ga - \frac{1}{2} (r \frac{v}{r})^2 v^2 > \frac{4ga}{3} so v > 2 \sqrt{ \frac{ga}{3}}

So then the condition on the initial velocity is: v > \sqrt{2ga - \frac{(r \omega)^2}{2}}

I think I may have worked it out. Kinetic Energy is given by: K = \frac{1}{2} I \omega^2 + \frac{1}{2} m v^2 = \frac{1}{2} (\frac{1}{2} m R^2) \omega^2 + \frac{1}{2} mv^2 Then: \Delta P = mg \Delta h = mga \Delta K = - \Delta P = -mga We want the kinetic energy of the...

I think that statement is still true regardless of the newer branches of mathematics (even though I don't find number theory particularly interesting). Besides, Gauss doesn't seem like a man who would take back something he has said.

Homework Statement A uniform cylinder of radius R, length L and density \delta is rolling without slipping along a horizontal surface with constant centre of mass speed u at A. It then meets a step of height b. We wish to find the conditions under which the cylinder is able to continue past...