Recent content by Scigatt

Ok, thanks

How'd you use θ to get ab3a-1 = a3b3a-3?

Homework Statement Let G be a finite group whose order is not divisible by 3. Suppose (ab)3 = a3b3 (\foralla,b\inG) Prove G must be abelian. Known: G is a finite group o(G) not divisible by 3 (ab)3 = a3b3 for all a,b\inG Homework Equations θ:G → G s.t. θ(g) = g3 \forallg \in G...

Are you talking about octant in the plane or octants in space? I'm not sure how the 'mismatched' octants would lead to such an error. Here is the preliminary triple integral of the first integral: 8\int_{\theta = \frac{-\pi}{4}}^{\frac{\pi}{4}}\int_{r = 0}^{1} \int_{z = 0}^{\sqrt{1 - x^{2}}}\...

Homework Statement I was trying to find the volume of the intersection between 3 cylinders x^2 + y^2 = 1, y^2 + z^2 =1, and z^2 + x^2 =1. I set up the double integral in two different ways: 8\int_{\theta = \frac{-\pi}{4}}^{\frac{\pi}{4}}\int_{r = 0}^{1} \sqrt{1 - r^{2}\: cos^{2}\, \theta}\...

I think that this was the proof that office_shredder was hinting at. Hopefully there aren't any errors or gaps here: Let S be a subset of [0,1]. Consider a function f_{S}:[0,1] \rightarrow \{0,1\} such that x \in [0,1] implies f_{S}(x) = 1\ iff\ x \in S. If a subset S has two such functions...

I was talking about the first part only.

The question mentions nothing about square matrices specifically.

I think #1 is false, actually, unless they mean row-equivalent.

Remember that: e = \lim_{n\to\infty} \left( 1 + \frac{1}{n} \right)^n by definition. Also remember the laws for manipulating limits.

You're going about it completely the wrong way. Try moving the limit around in the original expression.

Hint:Try to get A+B by multiplying the terms implied in the problem statement.