High Quality Content by WIKIPEDIA articles!n mathematics, a partition of an interval [a, b] on the real line is a finite sequence of the form a = x0 < x1 < x2 < ... < xn = b. Such partitions are used in the theory of the Riemann integral, the Riemann-Stieltjes integral and the regulated integral. A refinement of a partition, P, is another partition, Q, of the given interval that 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.

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