Category:Definitions/Bounded Sequences
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This category contains definitions related to Bounded Sequences.
Related results can be found in Category:Bounded Sequences.
A special case of a bounded mapping is a bounded sequence, where the domain of the mapping is $\N$.
Let $\struct {T, \preceq}$ be an ordered set.
Let $\sequence {x_n}$ be a sequence in $T$.
Then $\sequence {x_n}$ is bounded if and only if $\exists m, M \in T$ such that $\forall i \in \N$:
- $(1): \quad m \preceq x_i$
- $(2): \quad x_i \preceq M$
That is, if and only if it is bounded above and bounded below.
Subcategories
This category has the following 2 subcategories, out of 2 total.
B
S
Pages in category "Definitions/Bounded Sequences"
The following 12 pages are in this category, out of 12 total.
B
- Definition:Bounded Complex Sequence
- Definition:Bounded Real Sequence
- Definition:Bounded Sequence
- Definition:Bounded Sequence in Metric Space
- Definition:Bounded Sequence in Normed Division Ring
- Definition:Bounded Sequence in Normed Vector Space
- Definition:Bounded Sequence/Complex
- Definition:Bounded Sequence/Metric Space
- Definition:Bounded Sequence/Normed Division Ring
- Definition:Bounded Sequence/Normed Vector Space
- Definition:Bounded Sequence/Real