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Ackermann's Generalized Exponential Notation

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Ackermann's Generalized Exponential Notation is a large number notation.[1]

Formula Edit

  • 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 Edit

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 notationEdit

  • \(g(2,b,c) = c^{b}\)
  • \(g(3,b,c) = c\uparrow\uparrow{b}\)
  • \(g(a,b,c) = c\uparrow^{a-1}{b}\)

Sources Edit

  1. Googology

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