Difference between revisions of "Least upper bound"
m |
I_like_pie (talk | contribs) |
||
| Line 2: | Line 2: | ||
| − | Given a [[subset]] <math>S</math> in some larger [[ordered set]] <math>R</math>, a '''least upper bound''' or | + | Given a [[subset]] <math>S</math> in some larger [[ordered set]] <math>R</math>, a '''least upper bound''', or [[supremum]], for <math>S</math> is an [[element]] <math>\displaystyle M \in R</math> such that <math>s \leq M</math> for every <math>s \in S</math> and there is no <math>m < M</math> with this same property. |
If the least upper bound <math>M</math> of <math>S</math> is an element of <math>S</math>, it is also the [[maximum]] of <math>S</math>. If <math>M \not\in S</math>, then <math>S</math> has no maximum. | If the least upper bound <math>M</math> of <math>S</math> is an element of <math>S</math>, it is also the [[maximum]] of <math>S</math>. If <math>M \not\in S</math>, then <math>S</math> has no maximum. | ||
Revision as of 21:49, 3 November 2006
This article is a stub. Help us out by expanding it.
Given a subset 
in some larger ordered set 
, a least upper bound, or supremum, for is an element 
such that 
for every 
and there is no 
with this same property.
If the least upper bound 
of is an element of , it is also the maximum of . If 
, then has no maximum.
