Difference between revisions of "Axiom of completeness"
From Maths
(Created page with "{{Stub page|grade=B|msg=Demote to grade C once fleshed out better}} <br/> : {{Caution|This is a really badly named property of the real numbers, although first years are often...") |
m (Typo) |
||
| Line 1: | Line 1: | ||
{{Stub page|grade=B|msg=Demote to grade C once fleshed out better}} | {{Stub page|grade=B|msg=Demote to grade C once fleshed out better}} | ||
<br/> | <br/> | ||
| − | : {{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]] | + | : {{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]]; it may be proved if one constructs [[the real numbers]] "properly"}} |
__TOC__ | __TOC__ | ||
==[[Axiom of completeness/Statement|Statement]]== | ==[[Axiom of completeness/Statement|Statement]]== | ||
Latest revision as of 13:06, 30 July 2016
Stub grade: B
This page is a stub
This page is a stub, so it contains little or minimal information and is on a to-do list for being expanded.The message provided is:
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; it may 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
(Unknown grade)
This page requires one or more proofs to be filled in, it is on a to-do list for being expanded with them.
Please note that this does not mean the content is unreliable. Unless there are any caveats mentioned below the statement comes from a reliable source. As always, Warnings and limitations will be clearly shown and possibly highlighted if very important (see template:Caution et al).
References
