**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: ◎_{3}by ◎_{2}, ◎_{4}by ◎_{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-1}s.

## Nesting Levels

It is easy to have up-arrow and ◎ levels.

█ 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 ◎
_{0}in the end, a █◎_{0}b = a █↑ b - if █ have ◎
_{█↑}in the end, a █◎_{█↑}b = a █CCC...CCC a with b Cs, where C is ◎_{█}.