User blog comment:P進大好きbot/What is the greatest ordinal notation now?/@comment-31966679-20180623154722/@comment-31966679-20180624001703

When you looked at my notation, I think you viewed it differently.

I did define \(a_{0}(n) = a(n) = lvl(n, n, n)\) where I showed a link to my first blog post, the level function where it defines lvl(x, y, z)

Also, I didn't use the factorial at all. I think you received the old version of the blog post so I'll define it again.

\(a_{0}(n) = a(n) = lvl(n, n, n)\) where lvl(x, y, z) is defined in my first blog post.

\(a^{x}(n) = a(a^{x - 1}(n)\)

\(a^{1}(n) = a(n)\)

\(F(x, a(n)) = F(x - 1, a^{x}(n))\)

\(F(0, a(n)) = a(n)\)

\(a_{\beta + 1}(n) = F(n, a_{beta}(n))\)

\(a_{\beta}(n) = F(n, a_{\beta[n]}(n)\)