Okay, so there’s a lot of notations in the field of googology, and today, we will be talking about Ackermann’s Generalized Exponential Notation.

I will refer to this as the AGEN function, but it is g(a, b, c).

The rules (well, the definition) of AGEN is as follows:

  • g(a, b, c) = g(a-1, g(a, b-1, c), c)
  • g(a, 0, c) = 1 (if b = 0, it equals out to 1.)
  • g(0, b, c) = b + c
  • g(1, b, c) = bc

Simple. Let’s try a couple examples!

g(2, 3, 1) = g(1, g(2, 2, 1), 1) = g(2, 2, 1) = g(1, g(2, 1, 1), 1) = g(2, 1, 1) = g(1, g(2, 0, 1), 1) = g(1, 1, 1) = 1.

Me, being the crazy fanatic of programming I am, created a program for this, but it kinda doesn’t work with big numbers.

g(3, 3, 3) = 3^27, or 3↑↑3.

From how the Wikia page described it, it’s like this:

g(a, b, c) = c ↑a-1 b

Why was it this simple…

Therefore, if c = 1, then g(a, b, c) = 1.

Now, you might be thinking, “what if both a and b were 0?”

And to that my friends, I say “That’s for the next post!”

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