What does equivalence class mean?

Definitions for equivalence class
equiv·a·lence class

This dictionary definitions page includes all the possible meanings, example usage and translations of the word equivalence class.


  1. equivalence classnoun

    Any one of the subsets into which an equivalence relation partitions a set, each of these subsets containing all the elements of the set that are equivalent under the equivalence relation.


  1. Equivalence class

    In mathematics, when the elements of some set S {\displaystyle S} have a notion of equivalence (formalized as an equivalence relation), then one may naturally split the set S {\displaystyle S} into equivalence classes. These equivalence classes are constructed so that elements a {\displaystyle a} and b {\displaystyle b} belong to the same equivalence class if, and only if, they are equivalent. Formally, given a set S {\displaystyle S} and an equivalence relation ∼ {\displaystyle \,\sim \,} on S , {\displaystyle S,} the equivalence class of an element a {\displaystyle a} in S , {\displaystyle S,} denoted by [ a ] , {\displaystyle [a],} is the set of elements which are equivalent to a . {\displaystyle a.} It may be proven, from the defining properties of equivalence relations, that the equivalence classes form a partition of S . {\displaystyle S.} This partition—the set of equivalence classes—is sometimes called the quotient set or the quotient space of S {\displaystyle S} by ∼ , {\displaystyle \,\sim \,,} and is denoted by S / ∼ {\displaystyle S/{\sim }} . When the set S {\displaystyle S} has some structure (such as a group operation or a topology) and the equivalence relation ∼ {\displaystyle \,\sim \,} is compatible with this structure, the quotient set often inherits a similar structure from its parent set. Examples include quotient spaces in linear algebra, quotient spaces in topology, quotient groups, homogeneous spaces, quotient rings, quotient monoids, and quotient categories.


  1. Equivalence class

    In mathematics, given a set X and an equivalence relation ~ on X, the equivalence class of an element n in X is the subset of all elements in X which are equivalent to n. Equivalence classes among elements of a structure are often used to produce a smaller structure whose elements are the classes, distilling a relationship every element of the class shares with at least one other element of another class. This is known as modding out by the class. The class may assume the identity of one of the original elements, as when fractions are put in reduced form.

How to pronounce equivalence class?

How to say equivalence class in sign language?


  1. Chaldean Numerology

    The numerical value of equivalence class in Chaldean Numerology is: 9

  2. Pythagorean Numerology

    The numerical value of equivalence class in Pythagorean Numerology is: 6


Find a translation for the equivalence class definition in other languages:

Select another language:

  • - Select -
  • 简体中文 (Chinese - Simplified)
  • 繁體中文 (Chinese - Traditional)
  • Español (Spanish)
  • Esperanto (Esperanto)
  • 日本語 (Japanese)
  • Português (Portuguese)
  • Deutsch (German)
  • العربية (Arabic)
  • Français (French)
  • Русский (Russian)
  • ಕನ್ನಡ (Kannada)
  • 한국어 (Korean)
  • עברית (Hebrew)
  • Gaeilge (Irish)
  • Українська (Ukrainian)
  • اردو (Urdu)
  • Magyar (Hungarian)
  • मानक हिन्दी (Hindi)
  • Indonesia (Indonesian)
  • Italiano (Italian)
  • தமிழ் (Tamil)
  • Türkçe (Turkish)
  • తెలుగు (Telugu)
  • ภาษาไทย (Thai)
  • Tiếng Việt (Vietnamese)
  • Čeština (Czech)
  • Polski (Polish)
  • Bahasa Indonesia (Indonesian)
  • Românește (Romanian)
  • Nederlands (Dutch)
  • Ελληνικά (Greek)
  • Latinum (Latin)
  • Svenska (Swedish)
  • Dansk (Danish)
  • Suomi (Finnish)
  • فارسی (Persian)
  • ייִדיש (Yiddish)
  • հայերեն (Armenian)
  • Norsk (Norwegian)
  • English (English)

Word of the Day

Would you like us to send you a FREE new word definition delivered to your inbox daily?

Please enter your email address:


Use the citation below to add this definition to your bibliography:


"equivalence class." Definitions.net. STANDS4 LLC, 2024. Web. 13 Jun 2024. <https://www.definitions.net/definition/equivalence+class>.

Discuss these equivalence class definitions with the community:


    Are we missing a good definition for equivalence class? Don't keep it to yourself...

    Image or illustration of

    equivalence class

    Credit »

    Free, no signup required:

    Add to Chrome

    Get instant definitions for any word that hits you anywhere on the web!

    Free, no signup required:

    Add to Firefox

    Get instant definitions for any word that hits you anywhere on the web!

    Browse Definitions.net


    Are you a words master?

    the substance that is acted upon by an enzyme or ferment
    A substrate
    B callathump
    C mumblety-peg
    D maculation

    Nearby & related entries:

    Alternative searches for equivalence class: