Recent content by datenshinoai

Homework Statement Assume S contained in R2 is bounded. Prove that if S is Riemann measurable, then so are its interior and closure 2. The attempt at a solution Proof: If S is Riemann measurable, its boundary is a zero set. Since the boundary of each open U in the int(S) is part of...

Real Analysis: What does it mean for the set of invertible nxn matrices to be open? Homework Statement The set of invertible nxn matrices is open in M, is it also dense?2. The attempt at a solution Let S = set of invertible nxn matrics, S contained in M Let A be any invertible element in S...

Homework Statement Let K: [0,1] x [0,1] -> R be a continuous function such that K(x,y) > 0 and the integral K(x,y) dy <= C < 1 (from 0 to 1) for all x within [0,1]. Let g:[0,1] -> R be any continuous Function. Show that there is a unique continuous function f:[0,1] -> R such that f(x)=...

Homework Statement Let {a_n} be the sequence 3, 4, 8, 17,..., where a_0 = 3 and a_n+1 = a_n + (n+1)^2, n greater than or equal to 0. Find a polynomial such that a_n = f(n) Homework Equations f(n) = summation from r=0 to infinity of C(n,r) delta^r a_0 The Attempt at a Solution I...

I'm not sure how to study for the test since the midterms are open book and open notes. I've been going over the homework, but are there other ways of studying? I'm going over covering compactness, differentiation and integration for the next midterm. Any addition help/advice/problems to look...

Perhaps my question really is, what is the definition of a zero set? The book doesn't have a clear definition.

Homework Statement Prove that the interval [0,1] is not a zero set. 2. The attempt at a solution Assume for contradiction that the interval [0,1] = Z is a zero set. This mean that given epsilon greater than 0, there is a countable coverage of Z by open intervals (ai, bi) (___I don't...

I'm completely stumped on three questions, please help... 1. Particle 1 of charge +1x10^-6C and particle 2 of charge -3.0x10^-6C are held at separation L=10.0cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2...