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For example, squares (resp. triangles) have 4 sides (resp. 3 sides); or compact (resp. Lindelöf) spaces are ones where every open cover has a finite (resp. countable) open subcover. sharp Often, a mathematical theorem will establish constraints on the behavior of some object; for example, a function will be shown to have an upper or lower bound.
Thesaurus Linguae Latinae. A modern english thesaurus. A thesaurus (pl.: thesauri or thesauruses), sometimes called a synonym dictionary or dictionary of synonyms, is a reference work which arranges words by their meanings (or in simpler terms, a book where one can find different words with similar meanings to other words), [1] [2] sometimes as a hierarchy of broader and narrower terms ...
arcosech – inverse hyperbolic cosecant function. (Also written as arcsch.) arcosh – inverse hyperbolic cosine function. arcoth – inverse hyperbolic cotangent function. arcsch – inverse hyperbolic cosecant function. (Also written as arcosech.) arcsec – inverse secant function. arcsin – inverse sine function. arctan – inverse ...
Synonym list in cuneiform on a clay tablet, Neo-Assyrian period [1] A synonym is a word, morpheme, or phrase that means precisely or nearly the same as another word, morpheme, or phrase in a given language. [2] For example, in the English language, the words begin, start, commence, and initiate are all synonyms of one another: they are ...
Similarly, the geometric mean of n positive real numbers is an n-ary function: (=) = . Note that a logarithm of the geometric mean is the arithmetic mean of the logarithms of its n arguments From a mathematical point of view, a function of n arguments can always be considered as a function of a single argument that is an element of some product ...
For example, when writing :, the intent is that and are types, while the arrow is a type constructor, specifically, the function type or arrow type. Similarly, the Cartesian product of types is constructed by the product type constructor .
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For example, if a bounded differentiable function f defined on a closed interval in the real line has a single critical point, which is a local minimum, then it is also a global minimum (use the intermediate value theorem and Rolle's theorem to prove this by contradiction). In two and more dimensions, this argument fails.