Step function: Difference between revisions

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===Variations in the definition===

Sometimes, the intervals are required to be right-open<ref>{{Cite web|url=http://mathworld.wolfram.com/StepFunction.html|title = Step Function}}</ref> or allowed to be singleton.<ref>{{Cite web|url=http://mathonline.wikidot.com/step-functions|title = Step Functions - Mathonline}}</ref> The condition that the collection of intervals must be finite is often dropped, especially in school mathematics,<ref>{{Cite web|url=https://www.mathwords.com/s/step_function.htm|title=Mathwords: Step Function}}</ref><ref>{{Cite web | title=Archived copy | url=https://study.com/academy/lesson/step-function-definition-equation-examples.html {{Bare| URLarchive-url=https://web.archive.org/web/20150912010951/http://study.com:80/academy/lesson/step-function-definition-equation-examples.html inline| access-date=August2024-12-16 2022| archive-date=2015-09-12}}</ref><ref>{{Cite web|url=https://www.varsitytutors.com/hotmath/hotmath_help/topics/step-function|title = Step Function}}</ref> though it must still be [[Locally finite collection|locally finite]], resulting in the definition of piecewise constant functions.

==Examples==