Partition of an interval

Definition

Let $a < b$ be real numbers. A partition of $[a, b]$ is a finite sequence of real numbers $P = (x_0, x_1, \dots, x_n)$ with $$a = x_0 < x_1 < \cdots < x_n = b.$$ The intervals $[x_{i-1}, x_i]$ for $i = 1, \dots, n$ are the subintervals of $P$.