Boredom in Math Class Has Some *Interesting* Results

I got bored in Diffy Q's today, so I made up a new function. It is a sort of step function, but it increases so fast that it blows your mind. I had to make up some new notation for it. Here it is:

f(x) = x!_x

What it does is it takes the number x and puts it through x number of factorials. Thus,

If x = 1, f(x) = 1! = 1
If x = 2, f(x) = 2!! = 2
If x = 3, f(x) = 3!!! = 720!
If x = 4, f(x) = 4!!!! = (6.2 x 10²³)!!

Obviously this is an impressive function. Just imagine how big a number you'd get if you have x = Googolplex^{GoogolplexGoogolplexGoogolplex}. YIPERS!!