\*\*The Story of Large Numbers, a dive into the unknown\*\*
*The second chapter*

Today, I will introduce to you Knuth's up-arrow notation. You can think of it like a natural extension from addition, multiplication, and exponentiation. It goes like this:

with b amount of a's, we have
a*b = a+(a+(a+(...)))
a↑b = a^b = a*(a*(a*(...)))
a↑↑b = a↑(a↑(a↑(...)))
a↑↑↑b = a↑↑(a↑↑(a↑↑(...)))
a↑↑↑↑b = a↑↑↑(a↑↑↑(a↑↑↑(...)))
etc.
To compactify the notation, we write it as follows:

Perhaps, if you let your imagination stretch, we could try doing this:
g(g(g(g(10))))
But this isn't satisfying. What if... what if we do this instead?
[g^10](10)
Which would mean ten iterations of the g function. But wait! What about this?
[g↑↑10](10)
This would be expanded as follows:
= [g↑([g↑([g↑(...ten nestings...)](10))](10))](10)
In other words, you'd first try and solve [g^10](10), then call that number a1. Then let a2 = [g^a1](10), then a3 = [g^a2](10), etc. These will result in a crazy amount of nestings!