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Bounded set
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== Definition in the real numbers == [[File:Illustration of supremum.svg|thumb|upright=1.6|A real set with upper bounds and its [[supremum]].]] A set {{mvar|S}} of [[real number]]s is called ''bounded from above'' if there exists some real number {{mvar|k}} (not necessarily in {{mvar|S}}) such that {{math|''k'' β₯ '' s''}} for all {{mvar|s}} in {{mvar|S}}. The number {{mvar|k}} is called an '''upper bound''' of {{mvar|S}}. The terms ''bounded from below'' and '''lower bound''' are similarly defined. A set {{mvar|S}} is '''bounded''' if it has both upper and lower bounds. Therefore, a set of real numbers is bounded if it is contained in a [[interval (mathematics)|finite interval]].
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