How would I write mathematically (using set notation):
Let $F$ be the set defined by the distinct values of the function $f(x)$ for $a \le x \le b$ ($a$, $b$, $x$ and $f(x)$ are all natural integers).
I was thinking of:
$\mathbb{F} = \left \{ \forall x \in \left [a, b \right ] , a, b, x \in \mathbb{N}, f(x) \right \}$
But I'm not sure how to express the fact that the set should only contain distinct values, e.g. if $f(x)$ is equal to say 3, 4, 5, 3, 4 for $a$ through $b$, then $F = \{3, 4, 5\}$.
Can somebody help me out?