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Citation bot (talk | contribs) Add: s2cid, author pars. 1-1. Removed parameters. Some additions/deletions were actually parameter name changes. | You can use this bot yourself. Report bugs here. | Suggested by Abductive | All pages linked from cached copy of User:Abductive/sandbox | via #UCB_webform_linked 104/988 |
m The picture near the title does not display the graph of the function, but only an approximation to it. I changed the caption accordingly. |
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{{Use American English|date = March 2019}}
{{Short description|Continuous function that is not absolutely continuous}}
[[File:CantorEscalier.svg|thumb|right|400px|
In [[mathematics]], the '''Cantor function''' is an example of a [[function (mathematics)|function]] that is [[continuous function|continuous]], but not [[absolute continuity|absolutely continuous]]. It is a notorious counterexample in analysis, because it challenges naive intuitions about continuity, derivative, and measure. Though it is continuous everywhere and has zero derivative almost everywhere, its value still goes from 0 to 1 as its argument reaches from 0 to 1. Thus, in one sense the function seems very much like a constant one which cannot grow, and in another, it does indeed monotonically grow, by construction.
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