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  2. Python syntax and semantics - Wikipedia

    en.wikipedia.org/wiki/Python_syntax_and_semantics

    Python sets are very much like mathematical sets, and support operations like set intersection and union. Python also features a frozenset class for immutable sets, see Collection types. Dictionaries (class dict) are mutable mappings tying keys and corresponding values. Python has special syntax to create dictionaries ({key: value})

  3. List of set identities and relations - Wikipedia

    en.wikipedia.org/wiki/List_of_set_identities_and...

    It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations. The binary operations of set union and intersection satisfy many identities. Several of these identities or "laws" have well established names.

  4. Relation (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Relation_(mathematics)

    In mathematics, a relation denotes some kind of relationship between two objects in a set, which may or may not hold. [1] As an example, " is less than " is a relation on the set of natural numbers ; it holds, for instance, between the values 1 and 3 (denoted as 1 < 3 ), and likewise between 3 and 4 (denoted as 3 < 4 ), but not between the ...

  5. Relational operator - Wikipedia

    en.wikipedia.org/wiki/Relational_operator

    When it is desired to associate a numeric value with the result of a comparison between two data items, say a and b, the usual convention is to assign −1 if a < b, 0 if a = b and 1 if a > b. For example, the C function strcmp performs a three-way comparison and returns −1, 0, or 1 according to this convention, and qsort expects the ...

  6. Bijection - Wikipedia

    en.wikipedia.org/wiki/Bijection

    If X and Y are finite sets, then there exists a bijection between the two sets X and Y if and only if X and Y have the same number of elements. Indeed, in axiomatic set theory , this is taken as the definition of "same number of elements" ( equinumerosity ), and generalising this definition to infinite sets leads to the concept of cardinal ...

  7. Similarity measure - Wikipedia

    en.wikipedia.org/wiki/Similarity_measure

    Similarity between two sets The Jaccard index formula measures the similarity between two sets based on the number of items that are present in both sets relative to the total number of items. It is commonly used in recommendation systems and social media analysis [ citation needed ] .

  8. Semantic similarity - Wikipedia

    en.wikipedia.org/wiki/Semantic_similarity

    Semantic similarity is a metric defined over a set of documents or terms, where the idea of distance between items is based on the likeness of their meaning or semantic content [citation needed] as opposed to lexicographical similarity. These are mathematical tools used to estimate the strength of the semantic relationship between units of ...

  9. Myhill–Nerode theorem - Wikipedia

    en.wikipedia.org/wiki/Myhill–Nerode_theorem

    Given a language , and a pair of strings and , define a distinguishing extension to be a string such that exactly one of the two strings and belongs to . Define a relation ∼ L {\displaystyle \sim _{L}} on strings as x ∼ L y {\displaystyle x\;\sim _{L}\ y} if there is no distinguishing extension for x {\displaystyle x} and y {\displaystyle y} .