# Equality Relation

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An Equality Relation is a logical equivalence between two mathematical expressions.

**Context**- It is defined as [math]\displaystyle{ A = B }[/math] or [math]\displaystyle{ A \iff B }[/math] where [math]\displaystyle{ A }[/math] and [math]\displaystyle{ B }[/math] are two mathematical expressions, usually the combination of one or more binary operations.

**Example(s):**- Distributive Law, e.g. [math]\displaystyle{ (a \odot b)\star c = (a \star c) \odot (b \star c) }[/math]
- Associative Law, e.g. [math]\displaystyle{ (a \star b)\star c = a \star (b \star c) }[/math]

**Counter-Example(s):****See:**Equals Sign, Mathematical Expression, Mathematical Object.

## References

### 2016

- (Wikipedia, 2016) ⇒ https://en.wikipedia.org/wiki/equality_(mathematics) Retrieved:2016-5-24.
- In mathematics,
**equality**is a relationship between two quantities or, more generally two mathematical expressions, asserting that the quantities have the same value, or that the expressions represent the same mathematical object. The equality between*A*and*B*is written*A*=*B*, and pronounced*A*equals*B*. The symbol "=" is called an “equals sign”. Thus there are three kinds of equality, which are formalized in different ways.- Two symbols refer to the
*same object*. * Two sets have the*same elements*.^{[1]} - Two expressions evaluate to the
*same value*, such as a number, vector, function or set.

- Two symbols refer to the
- These may be thought of as the logical, set-theoretic and algebraic concepts of equality respectively.

- In mathematics,

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