[permalink] [id link]
A partition of X is a set P of nonempty subsets of X, such that every element of X is an element of a single element of P. Each element of P is a cell of the partition.
from
Wikipedia
Some Related Sentences
partition and X
This guarantees for any partition of a set X the existence of a subset C of X containing exactly one element from each part of the partition.
Since every equivalence relation over X corresponds to a partition of X, and vice versa, the number of possible equivalence relations on X equals the number of distinct partitions of X, which is the nth Bell number B < sub > n </ sub >:
Since each element of X belongs to a unique cell of any partition of X, and since each cell of the partition is identical to an equivalence class of X by ~, each element of X belongs to a unique equivalence class of X by ~.
partition and is
Finish your plumbing before you frame it in ( most economical framing is a thin non-bearing partition on either side of the pipes ).
note that the above online algorithm III is a special case of an algorithm that works for any partition of the sample into sets,:
where is the Boltzmann constant, T is temperature ( assumed to be a well-defined quantity ), is the degeneracy ( meaning, the number of levels having energy ; sometimes, the more general ' states ' are used instead of levels, to avoid using degeneracy in the equation ), N is the total number of particles and Z ( T ) is the partition function.
Its purpose is to unburden the application software programmer from the often complex details of the particular computer being used, including such accessories as communications devices, printers, device readers, displays and keyboards, and also to partition the computer's resources such as memory and processor time in a safe and stable manner.
Each civilian tile also has a Chinese name ( and common rough translation to English ): The 6-6 is tin ( 天 heaven ), 1-1 is dei ( 地 earth ), 4-4 is yan ( 人 man ), 1-3 is ngo ( 鵝 goose or 和 harmony ), 5-5 is mui ( 梅 plum flower ), 3-3 is cheung ( 長 long ), 2-2 is ban ( 板 board ), 5-6 is fu ( 斧 hatchet ), 4-6 is ping ( 屏 partition ), 1-6 is tsat ( 七 ) ( long leg seven ), and 1-5 is luk ( 六 ) ( big head six ).
Gas chromatography ( GC ) is based on a partition equilibrium of analyte between a solid stationary phase ( often a liquid silicone-based material ) and a mobile gas ( most often Helium ).
Following the partition of Ireland in 1922, it became the capital of the Irish Free State ( 1922 – 1949 ) and now is the capital of the Republic of Ireland.
In recent years there was a high demand for massively distributed databases with high partition tolerance but according to the CAP theorem it is impossible for a distributed system to simultaneously provide consistency, availability and partition tolerance guarantees.
partition and set
An equivalence relation partition of a set | partitions a set into several disjoint set | disjoint subsets, called equivalence class es.
In mathematics, an equivalence relation is a relation that, loosely speaking, partitions a set so that every element of the set is a member of one and only one cell of the partition.
Conversely, any surjection between sets determines a partition on its domain, the set of preimages of singletons in the codomain.
Let G denote the set of bijective functions over A that preserve the partition structure of A: ∀ x ∈ A ∀ g ∈ G ( g ( x ) ∈ ).
Therefore, the set of all equivalence classes of forms a partition of: every element of belongs to one and only one equivalence class.
Conversely every partition of comes from an equivalence relation in this way, according to which if and only if and belong to the same set of the partition.
In these applications, the set of all inputs is some sort of metric space, and the hashing function can be interpreted as a partition of that space into a grid of cells.
Conversely, from a partial order on a partition of a set S one can construct a preorder on S. There is a 1-to-1 correspondence between preorders and pairs ( partition, partial order ).
More generally, a Dedekind cut is a partition of a totally ordered set into two non-empty parts ( A and B ), such that A is closed downwards ( meaning that for all a in A, x ≤ a implies that x is in A as well ) and B is closed upwards, and A contains no greatest element.
Following the partition of Bengal in 1905, which was a strategy set out by Lord Curzon to weaken the nationalist movement, Tilak encouraged the Swadeshi movement and the Boycott movement.
In mathematics, a partition of unity of a topological space X is a set of continuous functions,, from X to the unit interval such that for every point,,
Some versions of DOS don't assign the drive letter, beginning with C :, to the first active primary partition recognized upon the first physical hard disk, but on the first primary partition recognized of the first hard disk, even if it is not set active.
Stirling numbers of the second kind count the number of ways to partition a set of n elements into k nonempty subsets.
A substantial part of early theoretical work on spin glasses dealt with a form of mean field theory based on a set of replicas of the partition function of the system.
partition and P
Further design modifications were made by Kreisel over the next ten years, and in the 1970s and 1980s by engineer John P. D ' Arcy ; record producer Daniel Levitin served as a consultant and " golden ears " for the design of the crossover network ( used to partition the frequency spectrum so that the subwoofer would not attempt to reproduce frequencies too high for its effective range, and so that the main speakers would not need to handle frequencies too low for their effective range ).
Another partition of the given interval, Q, is defined as a refinement of the partition, P, when it contains all the points of P and possibly some other points as well ; the partition Q is said to be “ finer ” than P. Given two partitions, P and Q, one can always form their common refinement, denoted P ∨ Q, which consists of all the points of P and Q, re-numbered in order.
partition and nonempty
In general, B < sub > n </ sub > is the number of partitions of a set of size n. A partition of a set S is defined as a set of nonempty, pairwise disjoint subsets of S whose union is S. For example, B < sub > 3 </ sub > = 5 because the 3-element set
A Dedekind cut in an ordered field is a partition of it, ( A, B ), such that A is nonempty and closed downwards, B is nonempty and closed upwards, and A contains no greatest element.
A partition of a set X is a set of nonempty subsets of X such that every element x in X is in exactly one of these subsets.
The Stirling numbers of the second kind count the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets.
0.176 seconds.