Bounded set

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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 ${\displaystyle \|\cdot \|}$. Then a set ${\displaystyle A\subset X}$ is bounded if there exists a real number M > 0 such that ${\displaystyle \|x\|\leq M}$ for all ${\displaystyle x\in A}$.