In mathematics, a partition Π of a closed interval [a, b] in the real numbers is a finite sequence of the form a = x0 < x1 < x2 <... < xn = b.
These partitions are used in Riemann integral theory and the Riemann-Stieltjes integral. Refining a Partition
A partition Π 'is said to be finer than a partition Π when Π is a subset of Π', that is, when the partition Π 'has the same points as Π and possibly some more. Examples
An example partition would be as follows: Given the interval [1, 2], a partition of said interval would be P = { 1 , 3 2 , 5 3 , 2 {\displaystyle 1,{\frac {3}{2}},{\frac {5}{3}},2} }. Another possible partition for the same interval would be P '= { 1 , 3 2 , 5 3 , 7 4 , 2 {\displaystyle 1,{\frac {3}{2}},{\frac {5}{3}},{\frac {7}{4}},2} }, with Π 'finer than .
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