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!”
Math we NEED to know 