User blog:AarexWikia04/Aperiation

Aperiation is the operator made by Aarex that go further than up-arrows.

Normal Definition
How we go further than up-arrow notation? Simple; just add ◎ between the numbers, but we need the definition. a◎b is equal to a↑↑↑ ... ↑↑↑a with b ↑s!

Combining Symbols
It is easy to combine symbol. ◎↑ nests over ◎ symbol, ◎↑↑ nests over ◎↑ symbol, etc.

We also have ◎◎, which is the limit of ◎↑↑...; ◎◎◎, which is the limit of ◎◎↑↑...; etc.

There we go! But we need rules and definition:

█ is the rest or full of the expression, must have ↑ or/and ◎ symbols.


 * if █ = empty, a █ b = a*b
 * if █ have ↑ in the end, a █↑ b = a █ a █↑ b-1
 * if █ have ↑ in the end and b is 1, a █↑ 1 = a
 * if █ have ◎ in the end, a █◎ b = a █↑↑↑...↑↑↑ a with b ↑s.

Levels
We would have 2nd level of ◎, called as ◎2. ◎2 works the same as ◎, but replace ↑ by ◎.

Then we also have: ◎3by ◎2, ◎4by ◎3, ....

█ is the rest or full of the expression, must have ↑ or/and ◎x symbols.


 * if █ = empty, a █ b = a*b
 * if █ have ↑ in the end, a █↑ b = a █ a █↑ b-1
 * if █ have ↑ in the end and b is 1, a █↑ 1 = a
 * if █ have ◎0 in the end, a █◎0 b = a █↑ b
 * if █ have ◎n in the end, a █◎n b = a █◎n-1◎n-1◎n-1...◎n-1◎n-1◎n-1 a with b ◎n-1s.

Nesting Levels
Coming soon