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# Partition

Partition has technical meanings in mathematics, computer science, and history.

## Mathematics

• A partition of a set X is given by 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 any set of functions whose sum is the constant function 1.
• 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.

## History

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