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  2. Infimum and supremum - Wikipedia

    en.wikipedia.org/wiki/Infimum_and_supremum

    A well-ordered set also has the least-upper-bound property, and the empty subset has also a least upper bound: the minimum of the whole set. An example of a set that lacks the least-upper-bound property is , the set of rational numbers.

  3. Essential infimum and essential supremum - Wikipedia

    en.wikipedia.org/wiki/Essential_infimum_and...

    In mathematics, the concepts of essential infimum and essential supremum are related to the notions of infimum and supremum, but adapted to measure theory and functional analysis, where one often deals with statements that are not valid for all elements in a set, but rather almost everywhere, that is, except on a set of measure zero.

  4. Uniform norm - Wikipedia

    en.wikipedia.org/wiki/Uniform_norm

    The perimeter of the square is the set of points in ℝ 2 where the sup norm equals a fixed positive constant. For example, points (2, 0), (2, 1), and (2, 2) lie along the perimeter of a square and belong to the set of vectors whose sup norm is 2.

  5. List of set identities and relations - Wikipedia

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

    This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.

  6. Set-theoretic limit - Wikipedia

    en.wikipedia.org/wiki/Set-theoretic_limit

    In mathematics, the limit of a sequence of sets,, … (subsets of a common set ) is a set whose elements are determined by the sequence in either of two equivalent ways: (1) by upper and lower bounds on the sequence that converge monotonically to the same set (analogous to convergence of real-valued sequences) and (2) by convergence of a sequence of indicator functions which are themselves ...

  7. Theory of basic human values - Wikipedia

    en.wikipedia.org/wiki/Theory_of_basic_human_values

    Circle chart of values in the theory of basic human values [1] The theory of basic human values is a theory of cross-cultural psychology and universal values developed by Shalom H. Schwartz. The theory extends previous cross-cultural communication frameworks such as Hofstede's cultural dimensions theory. Schwartz identifies ten basic human ...

  8. Head of key Japan opposition party admits to extra-marital affair

    www.aol.com/news/head-key-japan-opposition-party...

    Japanese lawmakers are set to decide at a special parliamentary session on Monday whether Prime Minister Shigeru Ishiba should stay as the country's premier after his scandal-tarnished coalition ...

  9. Signed measure - Wikipedia

    en.wikipedia.org/wiki/Signed_measure

    μ(E) ≥ 0 for each E in Σ such that E ⊆ P — in other words, P is a positive set; μ(E) ≤ 0 for each E in Σ such that E ⊆ N — that is, N is a negative set. Moreover, this decomposition is unique up to adding to/subtracting μ-null sets from P and N. Consider then two non-negative measures μ + and μ − defined by