In an introduction to the GNS construction, I'm told that the GNS construction is a generalization of the way that $L^{\infty} (X, \mu)$ has a repres...
Published: Sep 04, 2026
The transitive closure of a relation $R$ on set $A$ whose relation matrix My attempt: If I assumed node $(1, 2, 3)$, then given is: $R=\{(1, 2), (2, 3), (...
Published: Sep 04, 2026
Question: Let $P(n)$ be the statement that $1+\dfrac{1}{4}+\dfrac{1}{9}+\cdots +\dfrac{1}{n^2} <2- \dfrac{1}{n}$. Prove by mathematical induction. Use ...
Published: Sep 04, 2026
I want to solve $\int_C Im(z) dz$ where $C$ is the unit circle. The first thing is to parameterize the curve, $C$: $$ z(t)=e^{it} $$ where $0\leq t \leq 2...
Published: Sep 04, 2026
I know how to show that multiplying by an orthogonal matrix preserves the angle and distance between two vectors. I have seen everywhere that Orthogonal m...
Published: Sep 04, 2026
So it sounds like Higher Order Logic (HOL) and Type Theory are equivalent. Then there is Intuitionistic Logic and Intuitionistic Type Theory, but I'm...
Published: Sep 04, 2026
I am a student in calculus II. I'm now failing tests solely because I cannot factor; I understand everything else. This is compounded by the fact it ...
Published: Sep 04, 2026
For example: $\sin(15^\circ) = \frac{\sqrt{6}}{4} - \frac{\sqrt{2}}{4}$ $\sin(18^\circ) = \frac{\sqrt{5}}{4} - \frac{1}{4}$ $\sin(30^\circ) = \frac{1}{2}$...
Published: Sep 04, 2026
Find a linear dependence relation between the following vectors: x1 = (1, -1, 2) x2 = (-3, 2, 1) x3= (1, 2, -3) x4= (2, 3, 1) I've already created a ...
Published: Sep 04, 2026
the question How to simplify $\sin(x-y)\cos(y)+\cos(x-y)\sin(y)$ my steps I tried to use trig identities on the $\sin(x-y)$ and $\cos(x-y)$ and tried to d...
Published: Sep 04, 2026