Can anyone please help me with this?
Let $f,g_{1}, g_{2},\ldots,g_{k} \in \mathbb{Q}^{\mathbb{N}}$.
$f$ is a sum of $g_{1},g_{2},\ldots,g_{k}$ if for every natural number $n$
$f(n) = g_{1}(n) +g_{2}(n) + \cdots + g_{k}(n)$
a) Prove that for every $f \in \mathbb{Q}^{\mathbb{N}}$, $\exists$ three bijections $g_{1}, g_{2} , g_{3} \in \mathbb{Q}^{\mathbb{N}}$, such that $f$ is a sum of $g_{1}, g_{2},g_{3}$.
b) Give example for $f \in \mathbb{Q}^{\mathbb{N}}$, that is not a sum of two bijections $g_{1}, g_{2} \in \mathbb{Q}^{\mathbb{N}}$.
Thanks in advance.