# Bolzano-Weierstrass theorem for real sequences

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)



## [Bolzano-Weierstrass theorem for real sequences](https://ocme.evemisslab.com/en/atlas/atlas-bolzano-weierstrass-theorem-real/)

Every whole bounded real sequence has a convergent subsequence selected by an infinite strictly increasing index map.

atlas-bolzano-weierstrass-theorem-real · canonical_mko

[Bolzano-Weierstrass theorem for real sequences](https://ocme.evemisslab.com/en/mko/mko-bolzano-weierstrass-theorem-real/)

## Prerequisite nodes


- [Subsequence](https://ocme.evemisslab.com/en/atlas/atlas-subsequence/)
- [Sequence limits and exact tail cutoffs](https://ocme.evemisslab.com/en/atlas/atlas-sequence-limit/)
- [Real number](https://ocme.evemisslab.com/en/atlas/atlas-real-number/)
- [Supremum and infimum](https://ocme.evemisslab.com/en/atlas/atlas-supremum-and-infimum/)