## Basic Information[]

**Cantor's Absolute Infinity** is a number coined by **George Cantor** in the 19th century, which satisfies the full reflection principle: "All cardinality properties are satisfied in this number, [[1]] which held by a smaller cardinal."

It is also a paradoxical number which claim "no number can have a higher well-ordering in a set, and bigger than this."

There's way more "numbers" (Fictional Numbers) past Absolute infinity *[Ω]* and there's way less than

**[-Ω]**Even though Absolute infinity is a 'number', it can not be defined as it is paradoxical in nature because no one number could represent all 'real' numbers.

## Size[]

Absolute Infinity is past all the ordinals, cardinals, and finite numbers. It's size is so gargantuan it cannot be expressed, considered it's past anything reachable from below. Even still, it's just a Class 2 Infinity. It is basically the smallest of the infinities in Fictional Googology.

It would be only the biggest cardinal if one didn't define well-orderings and infinite axioms based on multi-sorted logic.

## Well-Definedness[]

Even though this server doesn't care about how well-defined something is, it's still good to provide an attempt at a definition. The definition for absolute infinity is a number which is bigger than any conceivable or inconceivable quantity, either finite or transfinite. (Edit from i do not like saws: There is a real definition but it's VERY hard to explain. (This then makes it defined)

## Trivia[]

- Introduces many paradoxes involving this number. One example is Burali-Forti Paradox, which involves the set of all well-ordering sets.
- This could actually be well defined, but if we wanna go past it, it's suddenly not well defined anymore.

**Ordinal Level 18**

**Absolute Infinity** - Ω+1 - Ω+2 - Ω+3 - Ω+5 -Ω+10 - Ω+100 - Ω+1000 - Ω+10^6 - Ω+10^9-Ω+10^12 - Ω+10^15 - Ω+10^100 - Ω+ω - Absolute Infinity times Two **[Ω2 / Ω+Ω / Ωx2]** - Ω2 - Ω3 - Ω10 - Ω100 - Ω1000 - Ω1,000,000 - Ω10^9 - Ω10^12 - Ω10^15 - Ω10^100 - Ωω - Absolutely Everything **[Ω ^{2}/ ΩΩ]** - Absolute Infinity Cubed

**[Ω**- Ω^4 - Ω^10 - Ω^100 - Ω^10^100 - Ω^ω - Ω^^2 - Ω^^3 - Ω^^ω

^{3}/ ΩΩΩ ]**[Absolute Infinity tetrated to ω / epsilon-Absolute onefinity]**- Absolute Infinity Pentated to 2 - Absolute Infinity Hexated to Two - AI^^^^^2 - AI^^^^^^2 - AI^^^^^^^2 - AI 17arrow 2 - AI 98 arrow 2 - AI 998 arrow 2 - AI 999,998 arrow 2 - AI 999,999,998 arrow 2 - AI expanded AI - AI exploded AI - 4 entry array of AI - 5 entry array of AI - 6 entry array of AI Ω1