Let $E$ be an empty set. Then, $\sup(E) = -\infty$ and $\inf(E)=+\infty$. I thought it is only meaningful to talk about $\inf(E)$ and $\sup(E)$ if $E$ is ...

Let $U(1000) =$ the multiplicative group of all integers less than and relative prime to $1000$. "Show that for every $x \in U(1000)$ it is true that $x^{...

I'm trying to help my daughter with her math homework and after scouring google and websites I find I truly do not understand how to complete this ev...

I understand that a complex number $n = a + bi$ is defined as having real $a,b$ with $i = \sqrt{-1}$. However what I don't understand is the why. Why...

Given 3 points, $(x_1, y_1), (x_2, y_2), (x_3, y_3)$, how might I find an equation intersecting all of these points? Given just 2 points, to find a linear...

Suppose I have a few ecuations: $$\cos^2(x) = \sin(x)\cos(x) \Rightarrow cos(x) = sin(x) $$ $$ x^2 + 3x \ge 2x \Rightarrow x(x+3) \ge 2x \Rightarrow x+3 \...

Hello I am engineering student. I need help understanding basic of matrix plotting. Currently I am learning about vectors and I wonder how they are repres...

Finally got to double angles. Anyways I need to show that these are identities. $$\sin(4x) = 4 \sin(x) \cos(x) \cos(2x)$$ The book does some magic and get...

$\textrm{Definition:}$ An infinite structure $\mathcal{M}$ is said to be minimal if every definable subset with parameters is finite or cofinite. $\textrm...

Particle, initially at rest travels in a straight line and its acceleration satisfies $$a=0.1(t-5)^2 $$for $0\leq t\leq5$ Find its average speed. during t...