Prove that every finite set is bounded.
Any ideas?
Assuming we are in $\displaystyle \mathcal{R}^1$.
Suppose we have a finite set A = $\displaystyle \left\{ {x_1 ,x_2 ,x_3 , \cdots ,x_n } \right\}$.
We form the number $\displaystyle \mathcal{B} = \sum\limits_{k = 1}^n {\left| {x_k } \right|} $
Is $\displaystyle \mathcal{B}$ a bound for $\displaystyle A$?