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 $\closedint a b$.

This page needs proofreading. In particular: Complete guess. Don't know whether this is accurate or not -- not sure how it works precisely at the $b$ end of the interval. If you believe all issues are dealt with, please remove {{Proofread}} from the code. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Proofread}} from the code.

Also known as

Some sources use the term partition for the concept of a subdivision.

However, the latter term has a different and more general definition, so its use is discouraged on $\mathsf{Pr} \infty \mathsf{fWiki}$.

Some use the term dissection, but again this also has a different meaning, and is similarly discouraged on $\mathsf{Pr} \infty \mathsf{fWiki}$.