# Partition

In general, a partition is a splitting into parts.

The word partition has technical meanings in architecture (including naval architecture), mathematics, computer science, politics, law, and music.

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## Mathematics

• A partition of a set X is a collection of non-empty subsets of X such that every element of X belongs to one and only one of the subsets.
• A partition of a number is a way to write a positive integer as a sum of other positive integers.
• The partition function in number theory is the function which for every positive integer gives the number of different ways to partition that number (in the sense above).
• A partition of unity is a set of functions whose sum is the constant function 1. The functions may be required to have additional properties such as continuity, smoothness, or non-negativity.
• The PARTITION problem is to divide a list of positive integers into two parts so that the sums of the numbers in the two parts are equal. It is a common example of an NP-complete problem, often useful in proving that other problems are NP-complete.
• A partition of an interval [a, b] on the real line is a finite increasing sequence of numbers a = x0 < x1 < ... < xn−1 < xn = b. Such partitions are used in the theory of the Riemann integral and the Riemann-Stieltjes integral, and in numerical computations with such integrals.

## Computer science

• Partition (computing), the dividing of a hard disk's storage space into independent parts called "partitions".
• for dividing a big computer (e.g. a mainframe) into several independent virtual computers, see also LPAR, IBM mainframe, Sun E10.000, HP-UX. Some vendors (e.g. Sun) use the term domain instead of partition. Distinction is made between software partitioning, implemented in the operating system or software level, and hardware partitioning, implemented in the hardware and/or firmware.
• Partition also refers to an algorithm used in quicksort which separates a list into two sublists, those elements less than or equal to a value and those greater than it. It is also used in selection algorithms.
• Computing Theory defines a Partition as the division of a set of elements into subsets such that all elements in the set appear in one and only one subset.
• Partition (database) for splitting a database.

## Music

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