another definition of cofinality

Let $\kappa$ be a limit ordinal (e.g. a cardinal). The cofinality of $\kappa$ $\mathrm{cf}(\kappa )$ could also be defined as:

$$\mathrm{cf}(\kappa )=inf\{|U|:U\subseteq \kappa \text{ such that }supU=\kappa \}$$

($supU$ is calculated using the natural order of the ordinals). The cofinality of a cardinal is always a regular cardinal and hence $\mathrm{cf}(\kappa )=\mathrm{cf}(\mathrm{cf}(\kappa ))$.

This definition is equivalent to the parent definition.

Title	another definition of cofinality
Canonical name	AnotherDefinitionOfCofinality
Date of creation	2013-03-22 13:52:59
Last modified on	2013-03-22 13:52:59
Owner	x_bas (2940)
Last modified by	x_bas (2940)
Numerical id	9
Author	x_bas (2940)
Entry type	Definition
Classification	msc 03E04