Prove that a finite non empty set of real numbers in bounded . I'm trying to solve an exercise that is as follow:
let $S = \{a_1, a_2, a_3, ......, a_n\}$ be a finite nonempty set of real numbers.
show that S is bounded.
I know that to prove a set is bounded you need to prove that it is bounded from above and below, but i do not know how to use that in a mathematical way, how i'm i suppose to prove it?

You might let $M = |a_1|+|a_2|+\cdots+|a_n|$.  Then for any $i$, you have 
$$a_i \leq |a_i| \leq M,$$
so $M$ is an upper bound of $S$.  Similarly $-M$ is a lower bound.
