Making Big Numbers

The year was ~45^2, and I was in dire trouble. My large number skills were taking heavy hits, and I was in dire trouble when someone invoked Graham's Number.

Luckily, I had a Googological notation up my sleeve. One more powerful than Graham's Number. It's based upon hyper operators. Stay for...

Holo Notation
Let's start with the simple hyper operators:

x {4} y = x ^ x ... ^x with y x's

The observant of you will notice that this is tetration. We can continue this, with

x {5} y = x {4} x ... {4} x with y x's

This is also known as "pentation" (amusingly, Google spellcheck unhelpfully thought I wanted to type "penetration").

This can then be generalised to:

x {n} y = x {n-1} x ... {n-1} x with y x's

You could then, hypothetically, imagine a number such as x {y{y}y} x. This is simplified to x {{y}} x.

To simplify the writing of Graham's Number, I also defined a second type of Holo Notation, whereby

x {n} y = x <n-2> y

And, of course, we can extend that by

x <y<y>y> x = x <<y>> x

At this point, I was ready to beat back the Graham's Number. I defined 4 <<64>> 4. The Duseedu was born.