Definition:Subdivision (Real Analysis)/Normal Subdivision

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

Let $P = \left\{{x_0, x_1, x_2, \ldots, x_{n - 1}, x_n}\right\}$ form a (finite) subdivision of $\left[{a \,.\,.\, b}\right]$.

$P$ is a normal subdivision of $\left[{a \,.\,.\, b}\right]$ :
 * the length of every interval of the form $\left[{x_i \,.\,.\, x_{i + 1} }\right]$ is the same as every other.

That is, :


 * $\exists c \in \R_{> 0}: \forall i \in \N_{< n}: x_{i + 1} - x_i = c$