mathematics, an ordered pair (a, b) is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair (a, b) is different...

singleton and an ordered pair, respectively. Tuples may be formally defined from ordered pairs by recurrence by starting from ordered pairs; indeed, an n-tuple...

reflexive, antisymmetric, and transitive. A partially ordered set (poset for short) is an ordered pair P = ( X , ≤ ) {\displaystyle P=(X,\leq )} consisting...

in P {\displaystyle P} or P − {\displaystyle P^{-}} , for example the ordered pair ( 0 , 0 ) {\displaystyle (0,0)} . Then the integers are defined to be...

Cartesian product of two sets A and B, denoted A × B, is the set of all ordered pairs (a, b) where a is in A and b is in B. In terms of set-builder notation...

an ordered pair (a, b) has a as its first element and b as its second element, which means (a, b) ≠ (b, a). While the two elements of an ordered pair (a...

{\displaystyle x\cup x^{c}=V} . Ordered Pair: For each a {\displaystyle a} , b {\displaystyle b} , the ordered pair of a {\displaystyle a} and b {\displaystyle...

by pairs of real numbers x and y. The order of the components x and y is significant, so such a pair is also called an ordered pair. Such a pair is written...

edges, directed links, directed lines, arrows, or arcs), which are ordered pairs of distinct vertices: E ⊆ { ( x , y ) ∣ ( x , y ) ∈ V 2 and x ≠ y }...

ordered pair (a pair ( x , y ) {\displaystyle (x,y)} which is the same type as its projections) in NFU. It is convenient to use the Kuratowski pair in...