In mathematics, the phrase almost all has a number of specialised uses.
"Almost all" is sometimes used synonymously with "all but finitely many"; see almost.
In number theory, if P(n) is a property of positive integers, and if p(N) denotes the number of positive integers n less than N for which P(n) holds, and if
p(N)/N → 1 as N → ∞
(see limit), then we say that "P(n) holds for almost all positive integers n". 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.
As with the last development series, we continue to offer two versions of changelogs: a rather nice to read players changelog that only includes changes every player will probably notice and the (rather) complete changelog with (almost) all the details, which is likely to cause a serious headache...
A lot was changed since the start of the stable 1.4.x branch and since I am too lazy to list all the great changes in here, better have a look at the forum thread which describes the most important changes.
As with the last releases, we continue to offer two versions of changelogs: a rather nice to read players changelog that only includes changes every player will probably notice and the (rather) complete changelog with (almost) all the details, which is likely to cause a serious headache...
In mathematics, the phrase almost all has a number of specialised uses.
"Almost all" is sometimes used synonymously with "all but finitely many" or "all but a countable set"; see almost.
Occasionally, "almost all" is used in the sense of "almost everywhere" in measure theory, or in the closely related sense of "almost surely" in probability theory.
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