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 subdivision of $\left[{a \,.\,.\, b}\right]$'''.

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

That is, iff:


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

Historical note
The name normal subdivision was specifically coined for ProofWiki, as the writer of this page has not found a name for this concept in the literature.