# Definition:Subdivision (Real Analysis)/Infinite

## Definition

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

Let $x_0, x_1, x_2, \ldots$ be an infinite number of points of $\R$ such that:

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

Then $\left\{{x_0, x_1, x_2, \ldots}\right\}$ forms an **infinite 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.