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In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical object. [1] Equality between A and B is written A = B, and pronounced "A equals B". In this equality, A and B are distinguished by calling them left-hand side (LHS), and right-hand side (RHS).
Visual proof of the Pythagorean identity: for any angle , the point (,) = (, ) lies on the unit circle, which satisfies the equation + =.Thus, + =. In mathematics, an identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables ...
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
The equality relation is the only example of a both reflexive and coreflexive relation, and any coreflexive relation is a subset of the identity relation. The union of a coreflexive relation and a transitive relation on the same set is always transitive.
Today the commutative property is a well-known and basic property used in most branches of mathematics. The first recorded use of the term commutative was in a memoir by François Servois in 1814, [1] [10] which used the word commutatives when describing functions that have what is now called the commutative property.
Fundamental rule of proportion. This rule is sometimes called Means‐Extremes Property. [4] If the ratios are expressed as fractions, then the same rule can be phrased in terms of the equality of "cross-products" [2] and is called Cross‐Products Property.
In mathematics, the distributive property of binary operations is a generalization of the distributive law, which asserts that the equality (+) = + is always true in elementary algebra. For example, in elementary arithmetic , one has 2 ⋅ ( 1 + 3 ) = ( 2 ⋅ 1 ) + ( 2 ⋅ 3 ) . {\displaystyle 2\cdot (1+3)=(2\cdot 1)+(2\cdot 3).}
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive. The equipollence relation between line segments in geometry is a common example of an equivalence relation. A simpler example is equality. Any number is equal to itself (reflexive).