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The meaning of "negligible" depends on the mathematical context; for instance, it can mean finite, countable, or null. In contrast, " almost no " means "a negligible quantity"; that is, "almost no elements of X {\displaystyle X} " means "a negligible quantity of elements of X {\displaystyle X} ".
Negligence (Lat. negligentia) [1] is a failure to exercise appropriate care expected to be exercised in similar circumstances. [2]Within the scope of tort law, negligence pertains to harm caused by the violation of a duty of care through a negligent act or failure to act.
In set theory, when dealing with sets of infinite size, the term almost or nearly is used to refer to all but a negligible amount of elements in the set. The notion of "negligible" depends on the context, and may mean "of measure zero" (in a measure space), "finite" (when infinite sets are involved), or "countable" (when uncountably infinite sets are involved).
This leads to the definitions of negligible functions given at the top of this article. Since the constants ε > 0 {\displaystyle \varepsilon >0} can be expressed as 1 / poly ( x ) {\displaystyle 1/\operatorname {poly} (x)} with a constant polynomial, this shows that infinitesimal functions are a superset of negligible functions.
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 ...
In mathematics, a negligible set is a set that is small enough that it can be ignored for some purpose. As common examples, finite sets can be ignored when studying the limit of a sequence , and null sets can be ignored when studying the integral of a measurable function .
In the mathematical field of general topology, a meagre set (also called a meager set or a set of first category) is a subset of a topological space that is small or negligible in a precise sense detailed below. A set that is not meagre is called nonmeagre, or of the second category. See below for definitions of other related terms.
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 ...