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  2. Unordered pair - Wikipedia

    en.wikipedia.org/wiki/Unordered_pair

    An unordered pair is a finite set; its cardinality (number of elements) is 2 or (if the two elements are not distinct) 1. In axiomatic set theory, the existence of unordered pairs is required by an axiom, the axiom of pairing. More generally, an unordered n-tuple is a set of the form {a 1, a 2,... a n}. [5] [6] [7]

  3. Axiom of pairing - Wikipedia

    en.wikipedia.org/wiki/Axiom_of_pairing

    For example, to prove the case n = 3, use the axiom of pairing three times, to produce the pair {A 1,A 2}, the singleton {A 3}, and then the pair {{A 1,A 2},{A 3}}. The axiom of union then produces the desired result, {A 1,A 2,A 3}. We can extend this schema to include n=0 if we interpret that case as the axiom of empty set.

  4. Kripke–Platek set theory - Wikipedia

    en.wikipedia.org/wiki/Kripke–Platek_set_theory

    Theorem: If A and B are sets, then there is a set A×B which consists of all ordered pairs (a, b) of elements a of A and b of B. Proof: The singleton set with member a, written {a}, is the same as the unordered pair {a, a}, by the axiom of extensionality. The singleton, the set {a, b}, and then also the ordered pair

  5. Ordered pair - Wikipedia

    en.wikipedia.org/wiki/Ordered_pair

    The ordered pair (a, b) is different from the ordered pair (b, a), unless a = b. In contrast, the unordered pair, denoted {a, b}, equals the unordered pair {b, a}. Ordered pairs are also called 2-tuples, or sequences (sometimes, lists in a computer science context) of length 2. Ordered pairs of scalars are sometimes called 2-dimensional vectors.

  6. Category:Articles with example PHP code - Wikipedia

    en.wikipedia.org/wiki/Category:Articles_with...

    Main page; Contents; Current events; Random article; About Wikipedia; Contact us; Help; Learn to edit; Community portal; Recent changes; Upload file

  7. Room square - Wikipedia

    en.wikipedia.org/wiki/Room_square

    Each cell of the array is either empty or contains an unordered pair from the set of symbols; Each symbol occurs exactly once in each row and column of the array; Every unordered pair of symbols occurs in exactly one cell of the array. An example, a Room square of order seven, if the set of symbols is integers from 0 to 7:

  8. Graph (discrete mathematics) - Wikipedia

    en.wikipedia.org/wiki/Graph_(discrete_mathematics)

    A graph with three vertices and three edges. A graph (sometimes called an undirected graph to distinguish it from a directed graph, or a simple graph to distinguish it from a multigraph) [4] [5] is a pair G = (V, E), where V is a set whose elements are called vertices (singular: vertex), and E is a set of unordered pairs {,} of vertices, whose elements are called edges (sometimes links or lines).

  9. Talk:Unordered pair - Wikipedia

    en.wikipedia.org/wiki/Talk:Unordered_pair

    2 Unordered pairs and binary sets are different and distinct concepts