Category:Convergent Sequences (Metric Space)

From ProofWiki
Jump to navigation Jump to search

This category contains results about Convergent Sequences (Metric Space).
Definitions specific to this category can be found in Definitions/Convergent Sequences (Metric Space).

Let $M = \struct {A, d}$ be a metric space or a pseudometric space.

Let $\sequence {x_k}$ be a sequence in $A$.

$\sequence {x_k}$ converges to the limit $l \in A$ if and only if:

$\forall \epsilon \in \R_{>0}: \exists N \in \R_{>0}: \forall n \in \N: n > N \implies \map d {x_n, l} < \epsilon$


This category has only the following subcategory.

Pages in category "Convergent Sequences (Metric Space)"

The following 2 pages are in this category, out of 2 total.