11,687
pages
Copy notation
TypeLinear
Based onrepeating digits
Growth rate$$f_{\omega3}(n)$$

Copy notation is a notation created by the Googology Wiki user, "TechKon" (Formerly SpongeTechX) used to define copied or repeated digits/numbers.

## Definition

Copy notation simply defines the amount of digits in a number which are all the same. You can simplify the number $$5,555$$ with this notation by using $$n[m]$$. n represents the digit you are using, and the m represents the amount of them. In this case, $$5,555$$ would be equal to $$5[4]$$ in copy notation because there are four fives. $$8,888,888$$ would be equal to $$8[7]$$ because there are seven eights.

Basically, if $$n$$ is a value, $$m$$ repeated digits of $$n$$ = $$n[m]$$, or $$n[m]$$ = $$m$$ $$n$$'s in copy notation.

All of this applies for 2, 3, etc.-digit numbers. $$10[10]$$ = $$10,101,010,101,010,101,010$$. That is ten tens.

### Examples

• 2[4] = 2,222 or four twos
• 4[8] = 44,444,444 or eight fours
• 9[2] = 99 or two nines
• 15[12] = 151,515,151,515,151,515,151,515 or twelve fifteens

### Extension

SpongeTechX extended it to multiple brackets.

a[[b]] = a[a[...[a[a]]...]] with b a's

a[[[b]]] = a[[a[[...[[a[[a]]]]...]]]] with b a's

a[[[[b]]]] = a[[[a[[[...[[[a[[[a]]]]]]...]]]]]] with b a's

And so on. Now

defines a[b,c] = a[[...[c]...]] with b pairs of brackets.

Then:

a[b,c,1] = a[b,c]

a[b,c,d] = a[a[b,c,d-1],a[b,c,d-1],d-1]

a[b,c,d,1] = a[b,c,d]

a[b,c,d,e] = a[a[b,c,d,e-1],a[b,c,d,e-1],a[b,c,d,e-1],e-1]

And so on. Then one last extension:

a[b#c] = a[b,b,...,b,b] with c b's

a[b##1] = a[a[b#b]#a[b#b]]

a[b##2] = a[a[b##1]#a[b##1]]

a[b##3] = a[a[b##2]#a[b##2]]

a[b##m] = a[a[b##(m-1)]#a[b##(m-1)]]

a[b###1] = a[a[b##b]##a[b##b]]

a[b###2] = a[a[b###1]##a[b###1]]

a[b###3] = a[a[b###2]##5[n###2]]

a[b###m] = a[a[b###(m-1)]##a[b###(m-1)]]

## Relation with Hypermathematics

Copy Notation has a relation with Hypermathematics. That is, a[b] is equal to a*b using Hypermathematics.