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  2. Infimum and supremum - Wikipedia

    en.wikipedia.org/wiki/Infimum_and_supremum

    The supremum (abbreviated sup; pl.: suprema) of a subset of a partially ordered set is the least element in that is greater than or equal to each element of , if such an element exists. [1] If the supremum of S {\displaystyle S} exists, it is unique, and if b is an upper bound of S {\displaystyle S} , then the supremum of S {\displaystyle S} is ...

  3. Glossary of mathematical symbols - Wikipedia

    en.wikipedia.org/wiki/Glossary_of_mathematical...

    A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...

  4. 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.

  5. 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. Not every ...

  6. Empty set - Wikipedia

    en.wikipedia.org/wiki/Empty_set

    The symbol is coded in LaTeX as ... That is, the least upper bound (sup or supremum) of the empty set is negative infinity, ... Modern Elementary Mathematics (2nd ed.).

  7. 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 ...

  8. List of mathematical abbreviations - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical...

    lim sup – limit superior. LLN – law of large numbers. ln – natural logarithm, log e. lnp1 – natural logarithm plus 1 function. ln1p – natural logarithm plus 1 function. log – logarithm. (If without a subscript, this may mean either log 10 or log e.) logh – natural logarithm, log e. [6] LST – language of set theory. lub – least ...

  9. Table of mathematical symbols by introduction date - Wikipedia

    en.wikipedia.org/wiki/Table_of_mathematical...

    The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.