# All Questions

8 views

### Self-duality in a lattice

Is there any self-dual lattice $(X,\le)$ such that there is not any self-duality $f:X\to X$ such that $f\circ f = 1_X$?
143 views

68 views

### Equality of real numbers whose squares sum to 1

I am helping a friend with homework and got stuck on the following problem. It doesn't seem like it should be that hard, I don't know why I'm having a hard time: For $a,b\geq0$, if $a^2+b^2=1$, then ...
36 views

### A certain two-step subgroup of a nilpotent group

Let $\Gamma$ be a finitely-generated, torsion-free, nilpotent group, of nilpotency class $n\ge 2$. Is there an $N \lhd \Gamma$, such that (i) $N$ is two-step nilpotent, (ii) $\Gamma / N$ is torsion ...
43 views

### How do I find the inverse of a $\cos^2 \theta$?

This was originally a physics question, but the math is what is throwing my brain into loops. Basically, I need to find $\theta$: $$\frac{7}{8}= \cos^2(\theta)$$
7 views

### Intersections on General Nonsingular Projective Varieties

Let $X$ be a nonsingular, integral projective variety of dimension at least 2 over $k$ algebraically closed. Let $Y$ and $Z$ be two codimension 1 subschemes (effective Weil divisors) of $X$. Must they ...
57 views

### determining $n$ in a given sequence $\frac{1+3+5+…+(2n-1)}{2+4+6+…+(2n)} =\frac{2011}{2012}$

Given that: $$\frac{1+3+5+...+(2n-1)}{2+4+6+...+(2n)} =\frac{2011}{2012}$$ Determine $n$. The memorandum says the answer is 2011 but how is that so? Where did I go wrong?
9 views

### limits changed F(g(x))=F(lim G(x))

lim x tends to 0(F(G(x))=F(lim x tends to 0(G(x))) I have seen this step in a derivation of a result which is not the point of interest here. The book wrote the reason for it was that it is when F ...
520 views

### Simplify $\frac{9}{2}(1 + \sqrt 5)\sqrt{10 - 2\sqrt 5} + 9\sqrt{5 + 2\sqrt 5}$

Simplify $\displaystyle{\frac{9}{2}(1 + \sqrt 5)\sqrt{10 - 2\sqrt 5} + 9\sqrt{5 + 2\sqrt 5}}$. I get this when I was doing another Q, but I don't know how to further simplify it. Can anyone help me, ...
140 views

### Solving $a(x+2)=\pi-cy$ for $x$, arrived at an answer different from the one in the book

In an algebra review book, one exercise asked to solve for $x$: $$a(x+2)=\pi-cy$$ I arrived at the following: $$x=\frac{\pi-cy}{a}-2$$ The book stated the correct answer is: $$x=\frac{\pi-cy-2a}{a}$$ ...
150 views

### Vector calculus and Frenet-Serret equations

I have shown the first two equality and I am working on the showing the 1st equals the 3rd. \begin{alignat*}{4} \frac{1}{\rho}\hat{\mathbf{{n}}} &= \frac{d\hat{\mathbf{{u}}}}{ds} &{}= ...
14 views

### General lists of techniques to prove whether a set is a generator of a matrix group

It seems like a rather common problem in group theory, at least in undergraduate maths, to check whether a set is a generator of a group. The question is usually as follow: Given a group $G$, and a ...
53 views

### How many times can transitivity property be applied

Can transitivity property be applied for infinite number of times for a certain problem??