Category:Definitions/Convergent Sequences in Normed Division Rings
Jump to navigation
Jump to search
This category contains definitions related to Convergent Sequences in Normed Division Rings.
Related results can be found in Category:Convergent Sequences in Normed Division Rings.
Let $\struct {R, \norm {\, \cdot \,} }$ be a normed division ring.
Let $\sequence {x_n} $ be a sequence in $R$.
The sequence $\sequence {x_n}$ converges to the limit $x \in R$ in the norm $\norm {\, \cdot \,}$ if and only if:
- $\forall \epsilon \in \R_{>0}: \exists N \in \R_{>0}: \forall n \in \N: n > N \implies \norm {x_n - x} < \epsilon$
Pages in category "Definitions/Convergent Sequences in Normed Division Rings"
The following 5 pages are in this category, out of 5 total.
C
- Definition:Convergent Sequence/Normed Division Ring
- Definition:Convergent Sequence/Normed Division Ring/Definition 1
- Definition:Convergent Sequence/Normed Division Ring/Definition 2
- Definition:Convergent Sequence/Normed Division Ring/Definition 3
- Definition:Convergent Sequence/Normed Division Ring/Definition 4