Definition:Subdivision (Real Analysis)/Finite

Definition
Let $\closedint a b$ 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 $\set {x_0, x_1, x_2, \ldots, x_{n - 1}, x_n}$ form a finite subdivision of $\closedint a b$.

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.

Some sources do not define the concept of infinite subdivision, and so simply refer to a finite subdivision as a subdivision.