Sunday, January 4, 2009

Step Functions

Step functions can be seen as generalizations of characteristic functions.

Step functions can be expressed as b = {b sub a such that a has multiple definitions)

For example consider a set M equal to a coordinate [1,5] expressed on multiple sets Bsub1=[1,2]

Now let all the sub numbers be defined on the y axis as follows

The resulting graph would be a series from 1 to 5 on the horizontal x axis (set A) with a line going from 1 to 2 at point 3 on the y axis, and another line going from 2 to 4 at point 4 on the y axis, and then another line completing the "step" to 5 from 4 to 5 at point 2 on the y axis.

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