Definition:Subdivision (Real Analysis)

Definition
Let $\left[{a \,.\,.\, b}\right]$ be a closed interval of the set $\R$ of real numbers.

Let $x_0, x_1, x_2, \ldots, x_{n-1}, x_n$ be points of $\R$ such that:


 * $a = x_0 < x_1 < x_2 < \cdots < x_{n-1} < x_n = b$

Then $\left\{{x_0, x_1, x_2, \ldots, x_{n-1}, x_n}\right\}$ form a subdivision of $\left[{a \,.\,.\, b}\right]$.

Also known as
Some sources use the term partition for this, but the latter term has an alternative and more general definition so it is probably better not to use it.