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.
- These may be thought of as the logical, set-theoretic and algebraic concepts of equality respectively.
- 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.
- ↑ . . .