xkcd

Funny incoming.

And also, xkcd is here.

And no, I don’t know if that number is involved in this.

Remember Graham’s number? Let’s call it G.

I’ll have to define something.

Ackermann’s function.

If you know this, then great!

If not, then here it is.

Wilhelm Ackermann created a function named after himself. The function takes two parameters, m and n and here are three rules:

1. A(0, n) = n + 1
2. A(m + 1, 0) = A(m, 1)
3. A(m + 1, n + 1) = A(m, A(m + 1, n))

Fun fact: the Ackermann function was actually used in the IMO test for 1981. It asked you to determine the value of A(4, 1981).

The xkcd number is A(G, G).

There’s a different function for this, named gag(n), where gag(n) = A(n, n). gag(n) can also be defined as 2 ↑^n-2 (n + 3) – 3, so the xkcd number can be defined as 2 ↑^{G – 2} (G + 3) – 3.

While it is a step down from SSCG(3), it’s still huge.

I mean, it’s larger than Graham’s Number!

Wait.

Is it?

That’s a topic for another time.