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...
25 KB (3,802 words) - 11:59, 30 July 2024
Tuple (redirect from Ordered triple)
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...
16 KB (2,181 words) - 01:50, 15 July 2024
Integer (section Equivalence classes of ordered pairs)
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...
35 KB (3,941 words) - 03:46, 16 August 2024
reflexive, antisymmetric, and transitive. A partially ordered set (poset for short) is an ordered pair P = ( X , ≤ ) {\displaystyle P=(X,\leq )} consisting...
40 KB (5,391 words) - 19:53, 22 June 2024
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...
3 KB (339 words) - 05:30, 1 June 2024
New Foundations (section Ordered pairs)
{\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...
50 KB (8,043 words) - 18:58, 22 July 2024
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...
21 KB (2,821 words) - 15:28, 14 June 2024
<360^{\circ }} . Vectors can be specified using either ordered pair notation (a subset of ordered set notation using only two components), or matrix notation...
22 KB (2,979 words) - 14:51, 9 June 2024
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 }...
28 KB (3,689 words) - 00:52, 14 August 2024
Vector space (section Ordered pairs of numbers)
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...
87 KB (11,494 words) - 16:23, 2 August 2024