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AarexWikia04

  • I live in Georgia, USA
  • I was born on October 12
  • I am Male
  • AarexWikia04

    An new new aarexnumbers!

    November 16, 2016 by AarexWikia04

    Today, I made new site using new Google Sites, so click here. It have AAN main page only so stay tuned.

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  • 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.

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  • AarexWikia04

    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 ◎, …




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  • AarexWikia04

    Aarex Cardinal

    July 29, 2016 by AarexWikia04

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

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  • 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)…



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