Could someone explain to me array notation

[Mk]

Could someone explain to me "array notation"

I found it here, but I still don't understand it. Though I probably don't need to know it, I want to. Also, will I encounter this anywhere else?

http://members.aol.com/hedrondude/array.html

 

[Gonzolo]

I understand it's useful for large number. I see these kinds of numbers as a field in pure math. I don't see how they can relate to physics or practical situations. From what I know, the largest quanties in physics can be delt with with exponentials (number of atoms in Universe, and such things). Large numbers may be encontered if tried to count something like how many total forces are presently acting in the Universe, but I'm willing to say most physicists never come by such numbers.

 

[chroot]

Yikes, this guy's a total crackpot. What he's describing is some strange machination he made up. No one in the world but him understands it, and it doesn't seem to have any benefits over normal scientific notation. Besides, look at the number of rules you'd have to learn to use it!

- Warren

 

[arildno]

I recall a notation for writing huge numbers that has been used in combinatorics.
(The actual symbol was an upwards arrow, but I don't know how to express that in Latex)

Let $$a?a=a^{a}$$
Let $$a?^{2}a=a?(a?a)$$
$$a?^{3}a=a?(a?^{2}a)$$
and so on.

One humongous number (the Ramsey number, I believe), can be expressed with the following sequence:
f(0)=3
$$f(n)=3?^{f(n-1)}3$$
The Ramsey number is given as f(63)..