# Monotone bounded sequence convergence theorem

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)



## [Monotone bounded sequence convergence theorem](https://ocme.evemisslab.com/en/atlas/atlas-monotone-sequence-convergence-theorem/)

A nondecreasing real sequence bounded above converges to the supremum of its terms; the nonincreasing bounded-below version converges to the infimum.

atlas-monotone-sequence-convergence-theorem · canonical_mko

[Monotone bounded sequence convergence theorem](https://ocme.evemisslab.com/en/mko/mko-monotone-sequence-convergence-theorem/)

## Prerequisite nodes


- [Supremum and infimum](https://ocme.evemisslab.com/en/atlas/atlas-supremum-and-infimum/)
- [Sequence limits and exact tail cutoffs](https://ocme.evemisslab.com/en/atlas/atlas-sequence-limit/)
- [Usual order on the real numbers](https://ocme.evemisslab.com/en/atlas/atlas-order-relation/)