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equivalence
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Figure 13: Constructions for the equivalence by dissection of (left) squares and (right) parallelograms (see text). Figure 12: Construction for the proof of equivalency of parallelograms by dissection (see text).
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equivalence

mathematics
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Figure 13: Constructions for the equivalence by dissection of (left) squares and (right) parallelograms (see text).
Figure 13: Constructions for the equivalence by dissection of (left) squares and (right) parallelograms (see text).

In mathematics, an equivalence relation is a way to generalize the concept of equality between elements of a set. It must satisfy three conditions:1
* Reflexivity: Every element is related to itself.
* Symmetry: If element A is related to element B, then B is also related to A.
* Transitivity: If A is related to B, and B is related to C, then A is related to C.12

An example is the congruence of triangles in geometry. Elements within a set that share an equivalence relation are said to belong to the same equivalence class.1

Two sets are considered equivalent if their members can be paired up exactly, with no members left over on either side. This concept applies to both finite and infinite sets.3

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4 Britannica Sources
  1. equivalence relation
  2. set theory - Equivalent sets
  3. set theory - Relations in set theory
  4. metalogic - Ultrafilters , ultraproducts , and ultrapowers

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