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Important Pages The Codex Wiki - Site FAQ - General Help Page- Tiering System - Civilization Tiering System - Rules for Codex Profiles - Common Editing Mistakes - Disclaimer - How to Handle Calculations - Universe - Multiverse - Omniverse - Projectile and Objects Feats - Dimensional Tiering Explanation - Common Terminology - Discussion Rules - Reference for Common Feats - Rules for Acceptable Profiles - Rules for Fanon Profiles - Misleading Titles - Mistranslations - Outside Wiki Standards - Statements - Verse Cosmology Categorizations - Fictional Universes
Terminology Alignment - Status - Protection Level - Threat Level - Cardinality - Grade - Dimensionality - Attack Potency - Durability - Speed - Reactions - Lifting Strength - Striking Strength - Range - Intelligence - Knowledge - Powers and Techniques - State of Being - Physiology - Equipment - No Limits Fallacy - Omnipotence - Cinematic Time - Canon - Crossover - Multipliers - Environmental Destruction - Bloodlust - Chain Reactions -Outside Help - Space - The Kardashev Scale - Infinity - Power Source - Light Speed - Requirements for Speed of Light/Faster Than Light Speeds
Standards Transcendence - Creation vs Destruction - Outlier - Ludonarrative Dissonance - Inconsistency - Plot-Induced Stupidity - Reality - Fiction Interaction - Powerscaling - Black Hole - Wormhole - Stabilization Feats - Merging Feats - Embodying Feats - Data World Standards - Dream World Standards - Standard Battle Assumptions - One-Shot - Speed Blitz - Penetration Damage - Blunt Force Damage - Death of the Author - Versus Threads - Information Pages - Light Dodging Feats - Lightning Standards - Timeless Void Standards
Formats Standard Format for Character Profiles - Standard Format for Factions - Standard Format for Cosmic Forces - Standard Format for Events - Standard Format for Verse Pages - Standard Format for Locations Profiles - Standard Format for Weapon Profiles - Standard Format for Powers and Abilities - Standard Format for Civilization Profiles - Standard Format for Category Names - Standard Templates For Tabbers


In mathematics, the cardinality of a set is a measure of the number of elements of the set. For example, the set A = {2, 4, 6} contains 3 elements, and therefore A has a cardinality of 3. The cardinality of a set A is usually denoted |A| with a vertical bar on each side; this is the same notation as absolute value, and the meaning depends on context.

The cardinality of the natural numbers is denoted aleph-null (ℵ0) while the cardinality of the real numbers is denoted by "c" and is also referred to as the cardinality of the continuum. Cantor showed, using the diagonal argument, that c >ℵ0.

The continuum hypothesis says that ℵ1 =2^ℵ0 i.e. 2^ℵ0 is the smallest cardinal number bigger than ℵ0, i.e. there is no set whose cardinality is strictly between that of the integers and that of the real numbers.

An infinite set A is called countably infinite (or countable) if it has the same cardinality as N. In other words, there is a bijection AN.

An infinite set A is called uncountably infinite (or uncountable) if it is not countable. In other words, there exists no bijection AN.

These definitions suggest that even among the class of infinite sets, there are different "sizes of infinity." In the sense of cardinality, countably infinite sets are "smaller" than uncountably infinite sets. Of course, finite sets are "smaller" than any infinite sets, but the distinction between countable and uncountable gives a way of comparing sizes of infinite sets as well. Below are some examples of countable and uncountable sets.


For the purpose and simplicity of the wiki, we divide Cardinality into easy to understand categories.

None: For characters at 11-C as they lack cardinality and energy altogether.

Finite: For characters that range all the way from Unknown to High 3-A, these characters have a finite set of cardinality.

ℵ0: For characters that range from High 3-A to 2-C, these characters affect an infinite sized universe contained within a finite sized volume.

Beyond ℵ0: For characters that range from 2-B to 2-A, these characters affect multiple universes contained within a space-time bubble.

ℵ1: For characters that are in 2-A+, this is where one affects an infinite sized multiverse or an infinite sized universe within a infinite sized volume.

ℵ2 or higher accessible: For characters that are in 1-C, this is where one approaches the larger uncountable infinities or transfinite cardinals within an accessible cardinal.

θ (Inaccessible Cardinal): For characters that are in 1-B, affecting things within an inaccessible cardinal.

->Ω (Approaching Absolute Infinity): For characters that are in 1-A, in this state the MUH is approaching absolute infinite, but never reaches it.

Ω (Absolute Infinity) : For characters that are in High 1-A, affecting things that deal with the absolute infinite.