an ordered pair, denoted (a, b), is a pair of objects in which their order is significant. The ordered pair (a, b) is different from the ordered pair (b...

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

also defined from ordered pairs by a recurrence starting from ordered pairs; indeed, an n-tuple can be identified with the ordered pair of its (n − 1) first...

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...

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...

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...

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...

{\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...

that, two ordered pairs are equal if and only if their first elements are equal and their second elements are equal. Formally, an ordered pair with first...

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 }...