I made something too large for me to understand.
The concept of this number is "repeating n times."
First, let's begin with this:
The concept of this number is "repeating n times"(I may repeat this sentence itself n times), so let's repeat SH(x) n times. But it's the first repeat, so I write like this:
(note: we can't write because there is not n)
Now you know what I will do next. Repeat that n times again.
I don't want to repeat such a formula, so I use n.
How big is this? That's easy.
It's too simple. Let's go larger.
The concept of this number is "repeating n times," that's why I repeated n times.
Now, SH(n,x) means "repeating (repeating n times) times." There are two "repeating (something) times" phrase. Now, you know where to diagonalizate. Yes. I will have n "repeating (something) times" phrase.
For more extension, I'll change the definition slightly:
This is larger than the first definition, but the number will have same number of up-arrows.
In this case, SH(n,0)has n times more repeat.
Now, I can translate "n 'repeating (something) times' phrase" in math languege.
Small letters are numbers and capital letters are "array" of numbers.
(note: N,M can be nothing and 0 in the second formula is the leftmost zero.)
Now, SH can have any number of numbers.
It's hard, but let's calculate simple one.
In the almost same reason,
It is still calculable, but now I stop calculating. "Defining a number" is important.
For my history, I will write old version of Ita-Chihaya number.
(note: I will write the Ita-Chihaya number version with Greek letters.)
Contnue to Ita-Chihaya number(2).