Math 2.0

Real functions Definition

Refinement of a partition

Builds on Partition of an interval

Definition

Let PP and QQ be partitions of [a,b][a, b]. The partition QQ is a refinement of PP if each point of PP is also a point of QQ.

Remarks

Any two partitions PP and QQ have a common refinement, made of the points of both. Refining a partition lowers the upper Darboux sum and raises the lower Darboux sum, or leaves them unchanged.

Reading path

To understand this page from the ground up, read these 2 pages in order. The foundations come first.

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Partition of an interval, definition, no evidence levelPartition of an inter…definitionRefinement of a partition, definition, no evidence levelRefinement of a parti…definition
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  1. Partition of an interval definition
  2. Refinement of a partition definition

Further reading

  1. Web https://en.wikipedia.org/wiki/Partition_of_an_interval, Refinement of a partition
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