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  2. Multiset - Wikipedia

    en.wikipedia.org/wiki/Multiset

    A multiset may be formally defined as an ordered pair (A, m) where A is the underlying set of the multiset, formed from its distinct elements, and : + is a function from A to the set of positive integers, giving the multiplicity – that is, the number of occurrences – of the element a in the multiset as the number m(a).

  3. Set (abstract data type) - Wikipedia

    en.wikipedia.org/wiki/Set_(abstract_data_type)

    A multiset is a special kind of set in which an element can appear multiple times in the set. Type theory. In type theory, sets are generally identified with ...

  4. Family of sets - Wikipedia

    en.wikipedia.org/wiki/Family_of_sets

    In set theory and related branches of mathematics, a family (or collection) can mean, depending upon the context, any of the following: set, indexed set, multiset, or class. A collection F {\displaystyle F} of subsets of a given set S {\displaystyle S} is called a family of subsets of S {\displaystyle S} , or a family of sets over S ...

  5. Permutation - Wikipedia

    en.wikipedia.org/wiki/Permutation

    If M is a finite multiset, then a multiset permutation is an ordered arrangement of elements of M in which each element appears a number of times equal exactly to its multiplicity in M. An anagram of a word having some repeated letters is an example of a multiset permutation.

  6. Disjoint sets - Wikipedia

    en.wikipedia.org/wiki/Disjoint_sets

    This definition of disjoint sets can be extended to families of sets and to indexed families of sets. By definition, a collection of sets is called a family of sets (such as the power set, for example). In some sources this is a set of sets, while other sources allow it to be a multiset of sets, with some sets repeated.

  7. Dershowitz–Manna ordering - Wikipedia

    en.wikipedia.org/wiki/Dershowitz–Manna_ordering

    In mathematics, the Dershowitz–Manna ordering is a well-founded ordering on multisets named after Nachum Dershowitz and Zohar Manna.It is often used in context of termination of programs or term rewriting systems.

  8. 15 over-the-top examples of wealth and luxury I saw on my ...

    www.aol.com/15-over-top-examples-wealth...

    Meanwhile, a trip to Aspen, Colorado, transformed my definition of luxury. In Paris and New York, five-star hotels and Michelin-star restaurants coexist alongside $1 pizza and cheap crepe carts.

  9. Amenable number - Wikipedia

    en.wikipedia.org/wiki/Amenable_number

    An amenable number is a positive integer for which there exists a multiset of as many integers as the original number that both add up to the original number and when multiplied together give the original number.