Definition:Subdivision (Real Analysis)/Infinite
< Definition:Subdivision (Real Analysis)
Let $\left[{a \,.\,.\, b}\right]$ 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 $\left\{{x_0, x_1, x_2, \ldots}\right\}$ forms an infinite subdivision of $\left[{a \,.\,.\, b}\right]$.
This article/section 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 are fairly certain that all issues are dealt with, please remove {{proofread}} from the code.
Some sources use the term partition for this, but the latter term has an alternative and more general definition so it is probably better not to use it.
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Definitions/Real Analysis
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