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Partition of an interval

In mathematics, a partition of an interval[a, b] on the real line is a finite sequencex0, x1, x2, …, xn of real numbers such that a = x0 < x1 < x2 < … < xn = b.In other terms, a partition of a compact interval I is a strictly increasing sequence of numbers (belonging to the interval I itself) starting from the initial point of I and arriving at the final point of I. Every interval of the form [xi, xi + 1] is referred to as a subinterval of the partition x. Refinement of a partitionAnother partition Q of the given interval [a, b] is defined as a refinement of the partitionP, if Q 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, in increasing order.

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