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Definition 7.1.1: Partition of an Interval

A partition P of the closed interval [a, b] is a finite set of points P = { x0, x1, x2, ..., xn} such that
a = x0 < x1 < x2 < ... < xn-1 < xn = b
The maximum difference between any two consecutive points of the partition is called the norm or mesh of the partition and denoted as | P |, i.e.
| P | = max { xj - xj-1, j = 1 ... n }
A refinement of the partition P is another partition P' that contains all the points from P and some additional points, again sorted by order of magnitude.
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