It says in the book that the set $F[a,b]$ of all functions on the interval $[a,b]$ is a vector space if pointwise addition and scalar multiplication are used.
I can't comprehend this statement very well.
If it means that the set of vectors form a space, then when I want to verify it through all the axioms, should I pick different functions and input some random number in the interval to be the arbitrary two different vectors or should I pick one function and input different numbers to be the arbitrary two different vectors?
I really hope that someone could understand what I'm asking here.
Please let me know if there is anywhere ambiguous in the question.