Ackermann's Generalized Exponential Notation is a large number notation.[1]
Formula[]
- g(a, b, c) = g(a-1, g(a, b-1, c), c)
- g(a ,0, c) = 1
- g(0, b, c) = b + c
- g(1, b, c) = bc
Joyce's more generalized Generalized Exponential Notation including nestings and roostings.
- g(a, b, c, d) = g(a - 1, b, c, g(b, c, d))
- g(a, b, c, d, e) = g(a - 1, b, c, g(b, c, d, e), e)
- g(a, b, c, d, e, f) = g(a - 1, b, c, g(b, c, d, e, f), e, f)
Examples[]
g(3,4,5) = 5 tetrated to 4
g(5, 3, 2) = g(4, g(5, 2, 2), 2) = 2 hexated to 3
In up-arrow notation[]
- \(g(2,b,c) = c^{b}\)
- \(g(3,b,c) = c\uparrow\uparrow{b}\)
- \(g(a,b,c) = c\uparrow^{a-1}{b}\)