# Convergence in a metric space

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.

[Catalogue presentation and source-binding data](https://ocme.evemisslab.com/data/i18n/catalogue.en.json)



## [Convergence in a metric space](https://ocme.evemisslab.com/en/atlas/atlas-metric-convergence/)

A sequence in a metric space converges to x when, for every positive epsilon, eventually all n≥N lie in the epsilon-ball around x.

atlas-metric-convergence · canonical_mko

[Convergence in a metric space](https://ocme.evemisslab.com/en/mko/mko-metric-convergence/)

## Prerequisite nodes


- [Metric space](https://ocme.evemisslab.com/en/atlas/atlas-metric-space/)
- [Sequence](https://ocme.evemisslab.com/en/atlas/atlas-sequence/)
- [Quantifiers and explicit domains](https://ocme.evemisslab.com/en/atlas/atlas-quantifier/)