User blog:MachineGunSuper/Infinite Line Function

IL(n) is defined as follows:

-Have an infinitely long line

-Make a segment as big as you want

-Find it's middle. Now, you will have 2 equal segments -Now, divide both segments into "n" smaller but equal segments. - Keep deviding the segments in "n" equal parts and labeling them in an unique way giving them consecutive states, keep on doing it nn times.
 * Label both of them in an unique way (different from each other). \(segment1\) now has state a, and \(segment2\) now has state a1
 * Label all the segments in an unique way, and continue on giving them consecutive states from a1.

- Count all the states (number of segments), and call that number sil(n). (small infinite line)

- Repeat the process defined above, but intead of dividing in "n" smaller segments, devide in sil(n) times, and also this time each segment gets sil(n) states.

- The number of states will now be called sil1(n)

- Repeat all the processes again, but each time replacing the number of divisions and states with the last sil(n) number.

For example, sil2(n) = Dividing in sil1(n) smaller segments and giving each segment sil1(n) states.

Define EIN(n) (extended infinite line) as siln+1(n)

EINa+1(n) = n copies of EINa(n)

Define HEIN(n) (Hyper Extended Infinite Line) as EINn+1(n)

HEINa+1(n) = n copies of HEINa(n)