Definition:Subdivision (Real Analysis)/Infinite
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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 $\mathsf{Pr} \infty \mathsf{fWiki}$.