---
tag: 0A8JNBGT2Z
kind: concept
name: Bounded sequence
msc: [40A05]
sources:
  - url: https://en.wikipedia.org/wiki/Bounded_function
    locator: lead section
---

## Summary

A bounded sequence is a real sequence whose terms all lie in one fixed interval. Boundedness is a necessary condition for convergence, and it is the hypothesis of the Bolzano–Weierstrass theorem. The node [[bounded sequence|05FQ3VGAR9]] gives the precise definition.