Let [a,b] be a closed interval. A set of n + 1 points x₀, x₁,…, x_n such that

is a partition of the interval [a,b]. A partition divides the interval into n subintervals [x_i,x_i + 1]. The norm (or mesh) of the partition P is equal to the length of the largest subinterval and is denoted by ∥P∥. Such partitions are used in defining Riemann sums (see integral).