Category:Definitions/Boundedness
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This category contains definitions related to Boundedness.
Related results can be found in Category:Boundedness.
Let $\struct {S, \preceq}$ be an ordered set.
Let $T \subseteq S$ be both bounded below and bounded above in $S$.
Then $T$ is bounded in $S$.
Subcategories
This category has the following 6 subcategories, out of 6 total.
Pages in category "Definitions/Boundedness"
The following 129 pages are in this category, out of 129 total.
B
- Definition:Bound
- Definition:Bound of Real-Valued Function
- Definition:Bound of Subset of Real Numbers
- Definition:Bounded
- Definition:Bounded Above
- Definition:Bounded Above Mapping
- Definition:Bounded Above Mapping/Real-Valued
- Definition:Bounded Above Mapping/Real-Valued/Unbounded
- Definition:Bounded Above Mapping/Unbounded
- Definition:Bounded Above Real-Valued Function
- Definition:Bounded Above Sequence
- Definition:Bounded Above Sequence/Real
- Definition:Bounded Above Sequence/Real/Unbounded
- Definition:Bounded Above Sequence/Unbounded
- Definition:Bounded Above Set
- Definition:Bounded Above Set/Real Numbers
- Definition:Bounded Above Set/Real Numbers/Unbounded
- Definition:Bounded Above Set/Unbounded
- Definition:Bounded Above Subset of Real Numbers
- Definition:Bounded Below
- Definition:Bounded Below Mapping
- Definition:Bounded Below Mapping/Real-Valued
- Definition:Bounded Below Mapping/Real-Valued/Unbounded
- Definition:Bounded Below Mapping/Real-Valued/Unbounded Below
- Definition:Bounded Below Mapping/Unbounded
- Definition:Bounded Below Real-Valued Function
- Definition:Bounded Below Sequence/Real/Unbounded
- Definition:Bounded Below Sequence/Unbounded
- Definition:Bounded Below Set
- Definition:Bounded Below Set/Real Numbers
- Definition:Bounded Below Set/Real Numbers/Unbounded
- Definition:Bounded Below Set/Unbounded
- Definition:Bounded Below Subset of Real Numbers
- Definition:Bounded Complex Sequence
- Definition:Bounded Mapping
- Definition:Bounded Mapping/Complex-Valued
- Definition:Bounded Mapping/Complex-Valued/Unbounded
- Definition:Bounded Mapping/Normed Division Ring
- Definition:Bounded Mapping/Real-Valued
- Definition:Bounded Mapping/Real-Valued/Attaining its Bounds
- Definition:Bounded Mapping/Real-Valued/Definition 1
- Definition:Bounded Mapping/Real-Valued/Definition 2
- Definition:Bounded Mapping/Real-Valued/Definition 3
- Definition:Bounded Mapping/Real-Valued/Unbounded
- Definition:Bounded Mapping/Unbounded
- Definition:Bounded Metric Space/Complex
- Definition:Bounded Metric Space/Complex/Unbounded
- Definition:Bounded Ordered Set
- Definition:Bounded Ordered Set/Real Numbers
- Definition:Bounded Ordered Set/Real Numbers/Definition 1
- Definition:Bounded Ordered Set/Real Numbers/Definition 2
- Definition:Bounded Ordered Set/Real Numbers/Unbounded
- Definition:Bounded Ordered Set/Unbounded
- Definition:Bounded Real Interval
- Definition:Bounded Real Sequence
- Definition:Bounded Real-Valued Function
- Definition:Bounded Real-Valued Function Attaining its Bounds
- Definition:Bounded Sequence
- Definition:Bounded Sequence in Metric Space
- Definition:Bounded Sequence in Normed Division Ring
- Definition:Bounded Sequence/Complex
- Definition:Bounded Sequence/Complex/Unbounded
- Definition:Bounded Sequence/Metric Space
- Definition:Bounded Sequence/Metric Space/Unbounded
- Definition:Bounded Sequence/Normed Division Ring
- Definition:Bounded Sequence/Normed Division Ring/Unbounded
- Definition:Bounded Sequence/Normed Vector Space
- Definition:Bounded Sequence/Normed Vector Space/Unbounded
- Definition:Bounded Sequence/Real
- Definition:Bounded Sequence/Real/Unbounded
- Definition:Bounded Sequence/Unbounded
- Definition:Bounded Subset of Real Numbers
I
L
- Definition:Limit of Real Function/Limit at Infinity/Negative/Decreasing Without Bound
- Definition:Limit of Real Function/Limit at Infinity/Negative/Increasing Without Bound
- Definition:Limit of Real Function/Limit at Infinity/Positive/Decreasing Without Bound
- Definition:Limit of Real Function/Limit at Infinity/Positive/Increasing Without Bound
- Definition:Locally Bounded
- Definition:Locally Bounded Mapping
- Definition:Locally Bounded/Family of Mappings
- Definition:Locally Bounded/Mapping
- Definition:Lower Bound
- Definition:Lower Bound of Mapping
- Definition:Lower Bound of Mapping/Real-Valued
- Definition:Lower Bound of Real Sequence
- Definition:Lower Bound of Real-Valued Function
- Definition:Lower Bound of Sequence
- Definition:Lower Bound of Sequence/Real
- Definition:Lower Bound of Set
- Definition:Lower Bound of Set/Real Numbers
- Definition:Lower Bound of Subset of Real Numbers
S
U
- Definition:Unbounded Above
- Definition:Unbounded Above Mapping
- Definition:Unbounded Above Real-Valued Function
- Definition:Unbounded Above Set
- Definition:Unbounded Above Subset of Real Numbers
- Definition:Unbounded Below
- Definition:Unbounded Below Mapping
- Definition:Unbounded Below Real-Valued Function
- Definition:Unbounded Below Sequence
- Definition:Unbounded Below Set
- Definition:Unbounded Below Subset of Real Numbers
- Definition:Unbounded Complex-Valued Function
- Definition:Unbounded Mapping
- Definition:Unbounded Ordered Set
- Definition:Unbounded Real Sequence
- Definition:Unbounded Real-Valued Function
- Definition:Unbounded Sequence
- Definition:Unbounded Subset of Real Numbers
- Definition:Uniformly Bounded
- Definition:Upper Bound
- Definition:Upper Bound of Mapping
- Definition:Upper Bound of Mapping/Real-Valued
- Definition:Upper Bound of Number
- Definition:Upper Bound of Real Sequence
- Definition:Upper Bound of Real-Valued Function
- Definition:Upper Bound of Sequence
- Definition:Upper Bound of Sequence/Real
- Definition:Upper Bound of Set
- Definition:Upper Bound of Set/Real Numbers
- Definition:Upper Bound of Subset of Real Numbers