Difference between revisions of "Partition of an interval"
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| − | A '''Partition of an interval''' is a way to formalise the intutive notion of ' | + | A '''Partition of an interval''' is a way to formalise the intutive notion of 'infinitesimal parts' of an interval. |
==Definition== | ==Definition== | ||
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Let <math>\mathcal{P}=\{x_0,x_1,\ldots,x_n\}</math> be a partition. | Let <math>\mathcal{P}=\{x_0,x_1,\ldots,x_n\}</math> be a partition. | ||
| − | A '''Tagged partition''' <math>\mathcal{\dot{P}}</math> is defined as the set of ordered pairs <math>\mathcal{\dot{P}}=\{([x_{i-1},x_i],t_i)\}_{i=1}^n</math>. The points <math>t_i</math> are called the '''Tags'''. | + | A '''Tagged partition''' <math>\mathcal{\dot{P}}</math> is defined as the set of ordered pairs <math>\mathcal{\dot{P}}=\{([x_{i-1},x_i],t_i)\}_{i=1}^n</math>. |
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| + | Where <math>x_{i-1}<t_i<x_i\forall t_i</math>. The points <math>t_i</math> are called the '''Tags'''. | ||
==See also== | ==See also== | ||
Revision as of 01:35, 16 February 2008
A Partition of an interval is a way to formalise the intutive notion of 'infinitesimal parts' of an interval.
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 n-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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