Cantor System

## Tiers

* **Universe Class:** This is the smallest destructive tier above **Multi-Galaxy Class**. This tier requires someone or something to be capable of outputting an infinite amount of energy, or to be capable of destroying all matter and energy in an infinitely large universe. Universes smaller than our own only apply for **Multi-Galaxy Class**.
* **Multiverse Class:**This refers to any character or item capable of destroying anywhere between two and one million universes. The separation of these universes doesn't matter, so long as each universe is infinitely large.
* **Multiverse Class+:** This tier refers to any character or item capable of destroying anywhere between one million and an infinite amount of universes.
* **Aleph-Null:** This tier contains everything from an infinite amount of universes to "∞∞∞... universes". A multiverse with infinite universes is contained within this, as is an infinite amount of multiverses, and an infinite amount of an infinite amount of multiverses, and so on. They are all in the same cardinality.
* **Omega:** ω1, by definition, exceeds all things contained in aleph-null. For simplicity, this tier contains everything from the "limit" of aleph-null onward.
* **Transcendental:** This tier refers to an absolutely infinite number of universes. Only characters or things beyond the concept of scale and logic can apply for this tier.

## Explanation

* **Universe to Multiverse+**

Our universe, while possibly finite, is most likely infinite. While models can be constructed that make finite universes, no evidence has been found to support these models. For this reason, we consider our universe to be infinite in size. Going off of this, the limit to the definition of "multiverse" would be an infinite number of universes.

* **Aleph-Null**

An aleph-null contains an infinite amount of numbers, or cardinals. All even numbers make up an aleph-null, as well as all odd numbers. However, both all even and odd numbers are still contained within an aleph-null. Even aleph-null+1 is contained in aleph-null.

From this, the logical conclusion is that even a number as large as an aleph-null2 is still considered to be "aleph-null". This is why this tier, for simplicity, is said to cover infinite multiverses as well as exponentially infinite multiverses.

* **Omega**

By definition, all possible orders and combinations of aleph-null are contained within ω1. From there, ω1 follows the same logic as aleph-null does. ω1+1 is still just "omega", and ω1ω is still just "omega".

Past this, you can come up with even higher sets that contain all possible orders of omega. And from there, even higher sets that contain all possible orders of *that*. So on and so forth, without limit. To avoid making an infinite amount of tiers, we count all sets larger than aleph-null as just apart of the "omega" tier.

* **Transcendental**

"Absolute infinite", as defined by Cantor, refers to a true infinity beyond all conceivable and non-conceivable levels of infinity. Since this concept lies beyond all numbers, logic, and math we consider it to be the highest tier possible.

## Further Information

Information on aleph numbers can be found in this Wikipedia article, as well as the Vsauce video below. Wikipedia also has information on absolute infinites, natural numbers, ordinal numbers, cardinal numbers, and even Cantor himself. Please also see their article on multiverse theory and the shape of the universe for further explanation on our earlier tiers.