User blog comment:Scorcher007/About Cofinality, sipmly/@comment-34422464-20190722143442/@comment-31580368-20190722151212

> You need sup at the beginning of the right hand side above.

Yes. It's typo.

For a clear explanation of why "cf(n) = 1, where n - successor ordinal"  can give the following examples:

ø = 0 = [] - axiom; 1 = [ø] = [0]; 2 = [0,1] = [ø,[ø]]; 3 = [0,1,2] = [ø,[ø],[ø,[ø]]] e.t.c.

ø - minimal element for creare any natural n > 0

ω - axiom; ω+1 = [ω]; ω+2 = [ω,[ω]]; ω+3 = [ω,[ω],[ω,[ω]]] e.t.c.

ω - minimal element for creare any ω+n, where n - natural, n > 0