User blog comment:MilkyWay90/Help with understanding Veblen array notation/@comment-30754445-20180811202716/@comment-31966679-20180818160107

"It should be sup(X_n) where X_1 = 0 and X_(n+1) = phi(X_n,0)

phi(1,0,0) = phi(phi(phi(...),0),0)"

The general definition I wrote down was:

phi(a, b, ..., c + 1, 0, ..., 0) with d+1 0s= sup{X_n} where:

X_1 = 0

X_(n + 1) = phi(a, b, ..., c, X_n, 0, ..., 0) with d + 1 0s

But, according to your definition:

X_(n + 1) = phi(a, b, ..., X_n, 0, ..., 0) with d 0s

It still doesn't work.

phi(1, 0, 0) = sup{X_n}

X_1 = 0

X_(n + 1) = phi(X_n, 0)

X_2 = phi(0, 0) = undefined

Did I get your definition wrong? And also, can you post rule 4? The one I've written down might have been wrong or I just am understanding wrong.