Difference between revisions of "Axiom of completeness/Statement"
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(Created page with "<noinclude> ==Statement== </noinclude>If {{M|S\subseteq\mathbb{R} }} is a ''non-empty set'' of real numbers that has an upper bound then{{rFAVIDMH}}: * {{M|\text{...") |
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==Statement== | ==Statement== | ||
</noinclude>If {{M|S\subseteq\mathbb{R} }} is a ''[[non-empty set]]'' of [[real numbers]] that has an [[upper bound]] then{{rFAVIDMH}}: | </noinclude>If {{M|S\subseteq\mathbb{R} }} is a ''[[non-empty set]]'' of [[real numbers]] that has an [[upper bound]] then{{rFAVIDMH}}: | ||
| − | * {{M|\text{Sup}(S)}} (the [[supremum]] of {{M|S}}) exists.< | + | * {{M|\text{Sup}(S)}} (the [[supremum]] of {{M|S}}) exists.<noinclude> |
==References== | ==References== | ||
<references/> | <references/> | ||
{{Theorem Of|Real Analysis}} | {{Theorem Of|Real Analysis}} | ||
</noinclude> | </noinclude> | ||
Latest revision as of 13:57, 2 June 2016
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
