So, you remember TREE(3)? It’s WAY, WAY BIGGER than that.
Now, to understand this, we need to know FRIEDMAN’S SSCG FUNCTION.
Information provided by Wikipedia and Googology Wikia.
A simple subcubic graph. If your first reaction was “What?” then you’re probably not alone. A simple subcubic graph is a finite “simple graph” with each vertices having a degree of at most three. So, no vertex in the graph is connected to more than three edges.
You know what? I can’t. here’s the links:
SSCG(0) = 2. SSCG(1) = 5. SSCG(2) = 322293793. Nah, just kidding. It’s about 3.241704 * 1035775080127201286522908640066, if I didn’t miss one. That’s insanely big, and that’s not even SSCG(3).
There’s also a similar function, SCG(n), and I don’t think it’s simple (see what I did? SubCubic Graph), and SCG(n) ≥ SSCG(3), but Adam P. Goucher could prove that SSCG(4n + 3) ≥ SCG(n).
Also, to put really large numbers into perspective, 1 billion factorial is approximately 1.57637137 * 108565705531, and that’s like nothing compared to even SSCG(2). Wow.
For SCG(0), it’s 6. It grows. REALLY FAST.
Next time, we’ll be exploring THE FAST-GROWING HIERARCHY.