# another definition of cofinality

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

 $\operatorname{cf}(\kappa)=\inf\{|U|:U\subseteq\kappa\text{ such that }\sup\;U=\kappa\}$

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

This definition is equivalent to the parent definition.

Title another definition of cofinality AnotherDefinitionOfCofinality 2013-03-22 13:52:59 2013-03-22 13:52:59 x_bas (2940) x_bas (2940) 9 x_bas (2940) Definition msc 03E04