Axiom of completeness/Statement

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Statement

If [ilmath]S\subseteq\mathbb{R} [/ilmath] is a non-empty set of real numbers that has an upper bound then[1]:

  • [ilmath]\text{Sup}(S)[/ilmath] (the supremum of [ilmath]S[/ilmath]) exists.

References

  1. Functional Analysis - Volume 1: A gentle introduction - Dzung Minh Ha