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Translations for „supremum“ in the English » Polish Dictionary (Go to Polish » English)

supremum MATH
kres górny (zbioru) m

Monolingual examples (not verified by PONS Editors)

English
Finding a supremum means to single out one distinguished least element from the set of upper bounds.
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However, as with the intermediate value theorem, an alternative version survives; in constructive analysis, any "located" subset of the real line has a supremum.
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Likewise, the "optimal lower bound" is the supremum of all lower bounds.
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This function is unbounded both from above and from below, so its supremum and infimum are and respectively.
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The weak global dimension of a ring is the supremum of the flat dimensions of its modules.
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If all directed subsets of a poset have a supremum, then the order is a directed complete partial order (dcpo).
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However, the product of an infinite set of metric spaces may not exist, because the distances in the base spaces may not have a supremum.
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In general, the supremum of any countable family of measurable functions is also measurable.
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The meet "a" b "and the join" a "b" of two elements coincide with their infimum and supremum, respectively, with respect to.
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If the supremum exists, it is unique, meaning that there will be only one supremum.
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