Category:Suprema
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This category contains results about Suprema in the context of Order Theory.
Definitions specific to this category can be found in Definitions/Suprema.
Let $\struct {S, \preceq}$ be an ordered set.
Let $T \subseteq S$.
An element $c \in S$ is the supremum of $T$ in $S$ if and only if:
- $(1): \quad c$ is an upper bound of $T$ in $S$
- $(2): \quad c \preceq d$ for all upper bounds $d$ of $T$ in $S$.
If there exists a supremum of $T$ (in $S$), we say that:
- $T$ admits a supremum (in $S$) or
- $T$ has a supremum (in $S$).
Subcategories
This category has the following 3 subcategories, out of 3 total.
E
I
S
Pages in category "Suprema"
The following 24 pages are in this category, out of 24 total.
C
F
I
S
- Set is Subset of Finite Suprema Set
- Set of Numbers of form n - 1 over n is Bounded Above
- Set of Rational Numbers Strictly between Zero and One has no Greatest or Least Element
- Sum of Indexed Suprema
- Supremum and Infimum are Unique
- Supremum does not Precede Infimum
- Supremum is not necessarily Greatest Element
- Supremum of Empty Set is Smallest Element
- Supremum of Singleton
- Supremum of Subset of Real Numbers May or May Not be in Subset
- Supremum of Suprema over Overlapping Domains
- Supremum of Union of Bounded Above Sets of Real Numbers