Difference between revisions of "Partition of an interval"
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| − | A '''partition of an interval''' is a division of an [[interval]] into several disjoint sub-intervals. Partitions of intervals arise in [[calculus]] in the context of [[Riemann integral]]s. | + | A '''partition of an interval''' is a division of an [[interval]] into several disjoint sub-intervals. Partitions of intervals arise in [[calculus]] in the context of [[Integral#Riemann Integral|Riemann integral]]s. |
==Definition== | ==Definition== | ||
Latest revision as of 19:34, 6 March 2022
A partition of an interval is a division of an interval into several disjoint sub-intervals. Partitions of intervals arise in calculus in the context of Riemann integrals.
Contents
Definition
Let ![$[a,b]$](http://latex.artofproblemsolving.com/8/e/c/8ecbd1ba3da8f2adef66a63f2ab32c47e63fa734.png)
be an interval of real numbers.
A partition 
is defined as the ordered 
-tuple of real numbers 
such that
Norm
The norm of a partition is defined as 
Tags
Let 
be a partition.
A Tagged partition 
is defined as the set of ordered pairs ![$\mathcal{\dot{P}}=\{([x_{i-1},x_i],t_i)\}_{i=1}^n$](http://latex.artofproblemsolving.com/1/e/4/1e4a621081b8c5c6b18dfd7163da5adfe7dcb1a2.png)
.
Where 
. The points 
are called the Tags.
See also
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