I am new to proofs and am still struggling to parse them. I am not looking for a proof to the following statement; just guidance as to where to start or what the shape of a proof for it looks like.
Prove that a subset $A$ of $\mathbb{R}$ is bounded if and only if there is $M ∈ \mathbb{R}$ such that $|x| ≤ M$ for all $x ∈ A$.
I know something is bounded if it has an upper and lower bound, and I have read axioms of fields and the definition of the absolute value.