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  2. Infimum and supremum - Wikipedia

    en.wikipedia.org/wiki/Infimum_and_supremum

    Consequently, the supremum is also referred to as the least upper bound (or LUB). [1] The infimum is, in a precise sense, dual to the concept of a supremum. Infima and suprema of real numbers are common special cases that are important in analysis, and especially in Lebesgue integration.

  3. Completeness (order theory) - Wikipedia

    en.wikipedia.org/wiki/Completeness_(order_theory)

    The supremum of B is then equal to the infimum of X: since each element of X is an upper bound of B, sup B is smaller than all elements of X, i.e. sup B is in B. It is the greatest element of B and hence the infimum of X. In a dual way, the existence of all infima implies the existence of all suprema.

  4. Glossary of order theory - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_order_theory

    For a poset P, a subset O is Scott-open if it is an upper set and all directed sets D that have a supremum in O have non-empty intersection with O. The set of all Scott-open sets forms a topology, the Scott topology. Semilattice. A semilattice is a poset in which either all finite non-empty joins (suprema) or all finite non-empty meets (infima ...

  5. Limit inferior and limit superior - Wikipedia

    en.wikipedia.org/wiki/Limit_inferior_and_limit...

    In mathematical analysis, limit superior and limit inferior are important tools for studying sequences of real numbers.Since the supremum and infimum of an unbounded set of real numbers may not exist (the reals are not a complete lattice), it is convenient to consider sequences in the affinely extended real number system: we add the positive and negative infinities to the real line to give the ...

  6. Limit-preserving function (order theory) - Wikipedia

    en.wikipedia.org/wiki/Limit-preserving_function...

    Roughly speaking, these functions map the supremum/infimum of a set to the supremum/infimum of the image of the set. Depending on the type of sets for which a function satisfies this property, it may preserve finite, directed, non-empty, or just arbitrary suprema or infima.

  7. Holiday Travel Forecast: Potential Problem Areas For The New Year

    www.aol.com/christmas-travel-forecast-potential...

    Whether you're heading home after the holidays or have festive plans to celebrate New Years Day, the busy holiday travel period continues, and weather may be a factor. For some, snow, rain ...

  8. Least-upper-bound property - Wikipedia

    en.wikipedia.org/wiki/Least-upper-bound_property

    In mathematics, the least-upper-bound property (sometimes called completeness, supremum property or l.u.b. property) [1] is a fundamental property of the real numbers. More generally, a partially ordered set X has the least-upper-bound property if every non-empty subset of X with an upper bound has a least upper bound (supremum) in X .

  9. The Best High-Yield Dividend ETF to Invest $2,000 in Right Now

    www.aol.com/best-high-yield-dividend-etf...

    JEPQ data by YCharts.. Long-term dividend yields. The monthly payouts added up to $5.38 per share over the last year, or a 10.7% yield against the current share price of approximately $58.