Bounded set

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Revision as of 07:19, 3 December 2007 by imported>Jitse Niesen (norm (mathematics) --> norm (mathematics))
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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 . Then a set is bounded if there exists a real number M>0 such that for all .