Linked from

The 30 pages that link to Ordered pair, each with the reason it gives.

• SetCompared with: Unlike set elements, entries in an ordered pair retain their positions.

• Cartesian coordinate systemBroader topic: In two dimensions, the pair gives a point’s horizontal and vertical coordinates.

• Equivalence relationRelated: A binary relation records related elements as ordered pairs.

• Set theoryRelated: Set-theoretic encodings of ordered pairs let relations and functions be represented as sets.

• FunctionRelated: Functions can be represented as sets of input-output ordered pairs.

• Zermelo–Fraenkel set theoryRelated: Pairing and other set operations encode ordered relationships without primitive tuples.

• Domain of a functionRelated: A function can be represented by input-output pairs, whose first coordinates form its domain.

• Cartesian productBroader topic: The product of two sets consists of ordered pairs, not unordered combinations.

• Coordinate geometryRelated: A point in the plane is represented by an ordered pair of coordinates.

• SubsetCompared with: An ordered pair is not generally a subset of its entries; its usual set encoding is a different construction.

• Function compositionRelated: The notation (f ∘ g)(x) encodes which function is applied first.

• SlopeRelated: Two ordered pairs supply the points used to calculate slope.

• Binary relationBroader topic: Each member of a binary relation records a related pair in a specific order.

• Transitive relationBroader topic: A relation records its links as ordered pairs, such as (a,b) and (b,c).

• Binary operationRelated: The operation receives ordered pairs, so reversing the inputs can change the output.

• Reflexive relationRelated: Each required self-relation appears as the ordered pair (a, a).

• Secant lineRelated: Each point on the curve is specified by an input-output ordered pair.

• Axiom of extensionalityRelated: Its encoding as a set must preserve identity through its elements, as extensionality requires.

• Axiom of pairingRelated: Pairing supplies sets used in common set-theoretic encodings of ordered pairs.

• Axiom of unionRelated: Pairing sets and taking their union is part of the standard construction of ordered pairs.

• ElementRelated: Ordered pairs can themselves be elements of sets, including Cartesian products.

• Antisymmetric relationBroader topic: Each instance of a binary relation is represented by an ordered pair.

• Distance formulaRelated: Each plane point is written as an ordered pair of coordinates.

• Graph of a functionRelated: The first coordinate is the input and the second is its function value.

• Symmetric relationBroader topic: The symmetry condition compares each pair with its reversal, (y, x).

• Membership relationRelated: Relations can be represented as sets of ordered pairs whose membership records which pairs satisfy them.

• Equality relationRelated: A relation includes ordered pairs, with equality containing precisely the pairs (x, x).

• Y-interceptRelated: The intercept’s first coordinate is zero, while its second gives its vertical position.

• Vector notationBroader topic: In two dimensions, a vector's components are often written as an ordered pair.

• Element of a setRelated: An ordered pair may itself be an element, while its entries need not be.