Definition and First Consequences
A function is called a step function if it can be written as
- for all real numbers
where are real numbers, are intervals, and is the indicator function of :
In this definition, the intervals can be assumed to have the following two properties:
- The intervals are disjoint, for
- The union of the intervals is the entire real line,
Indeed, if that is not the case to start with, a different set of intervals can be picked for which these assumptions hold. For example, the step function
can be written as
Read more about this topic: Step Function
Famous quotes containing the words definition and/or consequences:
“The physicians say, they are not materialists; but they are:MSpirit is matter reduced to an extreme thinness: O so thin!—But the definition of spiritual should be, that which is its own evidence. What notions do they attach to love! what to religion! One would not willingly pronounce these words in their hearing, and give them the occasion to profane them.”
—Ralph Waldo Emerson (1803–1882)
“There is a delicate balance of putting yourself last and not being a doormat and thinking of yourself first and not coming off as selfish, arrogant, or bossy. We spend the majority of our lives attempting to perfect this balance. When we are successful, we have many close, healthy relationships. When we are unsuccessful, we suffer the natural consequences of damaged and sometimes broken relationships. Children are just beginning their journey on this important life lesson.”
—Cindy L. Teachey. “Building Lifelong Relationships—School Age Programs at Work,” Child Care Exchange (January 1994)