Axiom of completeness
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Demote to grade C once fleshed out better
- Caution:This is a really badly named property of the real numbers, although first years are often given it as if it were an axiom but it can actually be proved if one constructs the real numbers "properly"
Contents
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.
Proof
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References
