almost all
almost all
English Definitions:
Almost all
In mathematics, the phrase "almost all" has a number of specialised uses. "Almost all" is sometimes used synonymously with "all but [except] finitely many" or "all but a countable set"; see almost. A simple example is that almost all prime numbers are odd, which is based on the fact that all but one prime number is odd. When speaking about the reals, sometimes it means "all reals but a set of Lebesgue measure zero". In this sense almost all reals are not a member of the Cantor set even though the Cantor set is uncountable. In number theory, if P is a property of positive integers, and if p denotes the number of positive integers n less than N for which P holds, and if , then we say that "P holds for almost all positive integers n" and write For example, the prime number theorem states that the number of prime numbers less than or equal to N is asymptotically equal to N/ln N. Therefore the proportion of prime integers is roughly 1/ln N, which tends to 0. Thus, almost all positive integers are composite, however there are still an infinite number of primes.
Almost all
In mathematics, the term "almost all" means "all but a negligible amount". More precisely, if X {\displaystyle X} is a set, "almost all elements of X {\displaystyle X} " means "all elements of X {\displaystyle X} but those in a negligible subset of X {\displaystyle X} ". 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 amount"; that is, "almost no elements of X {\displaystyle X} " means "a negligible amount of elements of X {\displaystyle X} ".
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"almost all." Kamus.net. STANDS4 LLC, 2024. Web. 25 Apr. 2024. <https://www.kamus.net/english/almost+all>.
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