If $A$ is an $m\times n$ matrix where $m\lt n$ The nonhomogeneous system $Ax=o$ has at least one solution and the homogeneous system $Ax=0$ has a unique s...

According to Wikipedia, there are uncountably many countable ordinals. What is the easiest way to see this? If I construct ordinals in the standard way, $...

I've read previous answers that state that the volume of a pyramid is $\frac{1}{3}$ (base $\times$ height). One way to visualize the volume of a squa...

I bought the fourth edition of Royden Real Analysis, this book is awesome and is quite different of third edition that has less excersices. I have the sol...

I have to play a lot with the $L^2$-norm defined as $\|w\|=\sqrt{\int_a^b \langle f,f \rangle}$. However, I don't understand the interpretation of th...

I am struggling with the concept of hermitian operators, symmetric operators and self adjoint operators. All of the relevant material seems quite self con...

My teacher gave me this limit to solve. She said it was meant to be really hard and she was right. I have no idea on how to attack this problem. Would any...

For $y=1/x^2$ As $x$ increases, the denominator ($x^2$) increases at an increasing rate. E.g. $1^2$ to $2^2$ is a difference of $3$, but $2^2$ to $3^2$ is...

This is something I thought about today but have no idea how to approach. We are given a right circular cone with lateral length L and angle at the base $...

I have the series $\sum_{n=0}^\infty \frac{n}{2^n}$. I must show that it converges to 2. I was given a hint to take the derivative of $\sum_{n=0}^\infty x...