Bounded set

In mathematics, a bounded set is any subset of a normed space whose elements all have norms which are bounded from above by a fixed positive real constant. In other words, all its elements are uniformly bounded in magnitude.

Formal Definition

Let X be a normed space with the norm $\|\cdot \|$. Then a set $A\subset X$ is bounded if there exists a real number M>0 such that $\|x\|\leq M$ for all $x\in A$.