Find the roots of unity for the p-adic numbers. Q is an abelian group. Prove that G is complete and that every connected component of G is a single element. Let R be the set of real numbers. Let X be a bounded subset of the real line.
P is a prism all of whose edges are tangent to a unit sphere.
T is a triangle of unit area. Choose two points in T independently, each with the uniform distribution. The line joining the points almost certainly divides the triangle into a triangle and a quadrilateral. Find their expected areas.