Definition:Subdivision (Real Analysis)/Infinite

Definition
Let $\closedint a b$ 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 $\set {x_0, x_1, x_2, \ldots}$ forms an infinite subdivision of $\closedint a b$.