Definition talk:Cofinality

This definition has been included in the Cardinals category. Can it be explained why this is the case? Is the cofinality itself a cardinal, and if so, can this be explained? --prime mover (talk) 08:37, 9 September 2012 (UTC)

The cofinality of an infinite cardinal is always an infinite cardinal. Cofinality is only interesting if studied in the context of infinite cardinals ($\operatorname{cf}(x+1) = 1$). --Andrew Salmon (talk) 08:54, 9 September 2012 (UTC)

Well yes, but this page defines the cofinality of an ordinal. Nothing is said about cardinals. --prime mover (talk) 12:25, 9 September 2012 (UTC)

Cofinality is central to the study of infinite cardinals. I will soon prove that the cofinality is always a cardinal. --Andrew Salmon (talk) 17:19, 9 September 2012 (UTC)

My point is that, in order to justify the presence of this definition in the Cardinals category, such an indication is necessary on the page itself. --prime mover (talk) 19:02, 9 September 2012 (UTC)

Fair enough. I will add this once the theorems are proved. --Andrew Salmon (talk) 20:31, 9 September 2012 (UTC)