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More on partitions

In general, we call subdivisions of an interval partitions. Partitions are usually specified by giving the set of endpoints of the subintervals, listed in increasing order, e.g. for our example of dividing the interval [0,4] into 4 equal subintervals we would write tex2html_wrap_inline307 .

To describe a general partition of the interval [a,b], we use subscript notation, tex2html_wrap_inline311 , to denote the i-th point in the partition. That is, a partition with N subintervals would be written tex2html_wrap_inline317 , where the points tex2html_wrap_inline319 satisfy


In the case of a uniform partition, there is a simple formula for tex2html_wrap_inline311 , which is


For example, there are five points in the uniform partition with four subintervals of the interval [0,4]. Plugging the values a=0, b=4, and N=4 into the equation above, we get


Sean O Anderson
Tue Nov 5 14:24:02 EST 1996