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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 ...
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 ...
Every non-empty subset of the real numbers which is bounded from above has a least upper bound.. 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.
As is often the case in measure-theoretic questions, the definition of essential supremum and infimum does not start by asking what a function does at points (that is, the image of ), but rather by asking for the set of points where equals a specific value (that is, the preimage of under ).
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 ...
Print/export Download as PDF; Printable version; In other projects Wikimedia Commons; Wiktionary; ... "T.9 B.1 List of combining characters/Variation selectors", ...
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Jargon often appears in lectures, and sometimes in print, as informal shorthand for rigorous arguments or precise ideas. Much of this uses common English words, but with a specific non-obvious meaning when used in a mathematical sense. Some phrases, like "in general", appear below in more than one section.
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