Partition of a Set is defined as "A collection of disjoint subsets of a given set. The union of the subsets must equal the entire original set." For example, one possible partition of $(1, 2, 3, 4, 5, 6 )$ is $(1, 3), (2), (4, 5, 6).$ Rudin, while defining integral on page $120$ starts like this,
Definition Let $[a, b]$ be a given interval. By a partition $P$ of $[a,b]$ we mean a finite set of points $x_0, x_1,..., x_n$, where $a=x_0\leq x_1\leq...\leq x_n=b$.
if all the points from $a$ to $b$ are in partition $P$ then where is the other partition, is it $\phi$?, not mentioned in the book.