# Fundamental sequence

From Cantor's Attic

(Redirected from Diagonalization)

A **fundamental sequence for an ordinal $\alpha$** is a sequence $(\alpha[\xi])_{\xi\in\beta}$ of some ordinal length, satisfying these properties:

- $\forall(\xi\in\beta)(\alpha[\xi]\in\beta)$
- $\textrm{sup}\{\alpha[\xi]:\xi\in\beta\}=\alpha$

The $\xi$th entry of the fundamental sequence of $\alpha$ is often denoted by $\alpha[\xi]$, but some authors have used other ways to denote it, such as $\{\alpha\}(\xi)$. [2]