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# AarexWikia04

• I live in Georgia, USA
• I was born on October 12
• I am Male
• ## An new new aarexnumbers!

November 16, 2016 by AarexWikia04

• ## Accouncement

September 18, 2016 by AarexWikia04

I will call it Accouncement because of account announcement.

So one of the admins in this wiki got IP-Blocked across all of Wikia sites. Why? Because of vandals.

FB100Z, if you seeing this, you will miss Cloudy.

• ## Aperiation

July 30, 2016 by AarexWikia04

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

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!

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.

We would have 2nd level of ◎, called as ◎2. ◎2 works the same as ◎, …

• ## Aarex Cardinal

July 29, 2016 by AarexWikia04

Delete this blog post. I know that T is Pi^2_0.

• ## Mapping Ordinals to Numbers

July 29, 2016 by AarexWikia04

I know how to map ordinals to base-n numbers with my definition. It will split to parts with milestone ordinals only.

Expression: ORD → NUM

ORD must be transfinite number and NUM is real numbers only.

It will be really easy. It only have 1 rule:

• ω → X = X

Where X can be like NUM.

This will have some rules because the operators. Let define ● as the rest of the ordinal expression.

• (empty expression) → X = 0
• ● ω → X = ● X → X
• ● ω + n → X = ● ω → X + n
• ● ω x 1 → X = ● ω → X
• ● ω x n → X = ● ω + (ω x n-1) → X
• ● ω ^ 1 → X = ● ω → X
• ● ω ^ n → X = ● ω x (ω ^ n-1) → X
• ε0 → X = ω ^ ω ^ ω ^ ... ^ ω ^ ω ^ ω → X with X ωs

For example: ε0 → 3

• ω ^ (ω ^ ω) → 3
• ω ^ (ω ^ 3) → 3
• ω ^ (ω x ω ^ 2) → 3
• ω ^ (ω x ω x ω ^ 1) → 3
• ω ^ (ω x ω x ω) → 3
• ω ^ (ω x ω x 3) → 3
• ω ^ (ω x (ω + ω x 2)…