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The equals sign, used to represent equality symbolically in an equation. In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical object.
A Greek mathematician Eudoxus provided a definition for the meaning of the equality between two ratios. This definition of proportion forms the subject of Euclid's Book V, where we can read: This definition of proportion forms the subject of Euclid's Book V, where we can read:
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 ...
By definition, equality is an equivalence relation, meaning it is reflexive (i.e. =), symmetric (i.e. if = then =), and transitive (i.e. if = and = then =). [33] It also satisfies the important property that if two symbols are used for equal things, then one symbol can be substituted for the other in any true statement about the first and the ...
In mathematics, Euler's identity [note 1] (also known as Euler's equation) is the equality + = where is Euler's number, the base of natural logarithms, is the imaginary unit, which by definition satisfies =, and
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).
Proof of the theorem. We need to prove that AF = FD.We will prove that both AF and FD are in fact equal to FM.. To prove that AF = FM, first note that the angles FAM and CBM are equal, because they are inscribed angles that intercept the same arc of the circle (CD).
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.