User blog:Primussupremus/Hypermathematics copy notation.

Yesterday I was browsing the main wiki when I came across the article on copy notation invented by wiki user Sponge Tech X. The notation is used to define repeated digits in a number for example 5[2]=55, this is an example of Hyper mathematics as it is based on concatenation the mathematical operation for gluing two numbers together.

Here is an example of copy notation as well as some extensions on it that I came up with or was inspired by.

1[1]=1

2[2]=22

3[3]=333

4[4]=4444

5[5]=55555

6[6]=666666

7[7]= 7777777

8[8]=88888888

9[9] = 999999999

10[10]=10101010101010101010

Here are some of my extensions to this

2[2[2]] = a chain of 22 2's or 2222222222222222222222.

2[2[2[2]]]= a chain of 2222222222222222222222 2's.

2[2[2[2[2]]]] = a chain of 2[2[2[2]]] 2's.

As this is getting quite cluttered I have come up with a solution instead of writing out all the numbers you just have to know how many pairs of braces there are.

For example: 2[2[2[2[2]]]] has 4 pairs of braces so you write it as 2[#4].

10 [#10] means would that there are 10 pairs of braces that make up this number.

The next thing I thought of when making extensions to this was how could I express things with 10[#100] pairs of braces?

10[#100]= 10[#100,1]

10[#10[#100]] means that there are 10[#100] pairs of braces so we call it 10[#100,2]

I even extended it beyond this so as to incorporate higher order iterations like the 10[#10,2]th iteration.

The way you it is like this 10[#100,2,(1)

Where (1) that you do the process of iteration 10[#100,2] times once.

10[#100,2,(1000) means that you do it 1000 times.