$\in$ - is a member of

$\forall$ - for all

$\exists$ - there exists

$\implies$ - implies

$=$ means two things are equal

$:=$ is the assignment operator - similar to the = sign in programming languages!

Mathematicians use interval notation for shorthand for ranges. $[]$ denotes that endpoints are included (it is closed), $()$ denotes that they are not.

For example:

$$ \begin{align*}&x \in [0,1] &&= &&&0 \leq x \leq 1 \\ &x \in [-10, 20) &&= &&&-10 \leq x < 20 \\ &x \in (-\infin, 0] &&= &&&x < 0 \end{align*} $$