Copy notation

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]##a[n###2]]
a[b###m] = a[a[b###(m-1)]##a[b###(m-1)]]
== Approximation ==
\(\frac{a+1}{10^{\left\lfloor\log a\right\rfloor}}10^{b(1+\left\lfloor\log a\right\rfloor)-1}\ge{a[b]}\ge\frac{a}{10^{\left\lfloor\log a\right\rfloor}}10^{b(1+\left\lfloor\log a\right\rfloor)-1}\)
\(a\uparrow\uparrow{b}\ge{a[[b]]}\)
\(a\uparrow^c{b}\ge{a[c,b]}\)
== Relation with Hypermathematics ==
Copy Notation has a relation with Hypermathematics. That is, a[b] is equal to a*b using Hypermathematics.
==Sources==
*Tech's Large Numbers
Category:Notations
Category:SpongeTechX