We consider the Euclidean space version of the Doob Dynkin lemma. In particular we first consider the real line, and the statement of the lemma becomes If...

Consider the family of sets $F = \{S_1, \dots, S_m\}$ $\forall m \in \mathbb{N}$, where $S_i$ is a set of elements $\forall i \leq m$. Let us define $C \s...

For the following two question Let P, Q, and R be logical statements. Use a truth table to prove that_______. Let P, Q, and R be statement variables, and ...

I have the integral $$\int x\log(x)\ dx,$$ and I need to solve it by substitution. I don't know why, if you substitute $x$ by $g(y)$ you have $x= e^y...

In finite geometry, the Fano plane is the finite projective plane with the smallest possible number of points and lines: 7 each. Why its automorphism grou...

The following is an excerpt from do Carmo's Differential Geometry of Curves and Surfaces about the first fundamental form: I don't understand wh...

I've been trying to translate the following sentences into quantified propositions by making sure I state all propositional functions that I use and ...

A teacher asked me to prove the well known Crossbar theorem. I tried it in the following way:- Given: If $D$ is in the interior of $\triangle ABC$, then p...

How can I know the values of: $\sin(i)$ and $\cos(i)$? I am studying complex variables for the first time, so I asked myself if these functions exist (con...

Finding $y$-intercepts is very easy on a TI-83/TI-84 calculator. All you have to do is graph the function and use 2nd $\to$ Trace $\to$ Value $\to$ $x=0$....