User blog comment:MilkyWay90/A new ordinal notation/@comment-32697988-20180718002157/@comment-31966679-20180718181556

Define the successor function as S(n) = n + 1. This can be applied to ordinals easily.

Then do Add(a, b) = S(S(S(...S(a)...))) with b Ss

Then define Multiply(a, b) as Add(a, Add(a, Add(... Add(a, Add(a, a))...))) with b as

After that, define Expo(a, b) = Mult(a, Mult(a, Mult(... Mult(a, Mult(a, a)) ...))) with b as

Then define Tetration(a, b) = Expo(a, Expo(a, Expo(... Expo(a, Expo(a, a)) ...))) with b as

\(\omega \uparrow \uparrow n\) = Tetration(w, n)