Latest revision as of 16:03, 10 July 2017

The Devil's staircase (also known as the Cantor function) is a function $c \colon [0,1] \rightarrow [0,1]$ can be expressed by the following rules:

Write $x$ in base-3.
If that representation of $x$ contains a $1$, replace every digit after the first $1$ with $0$'s.
Replace all $2$'s with $1$'s.
The resulting expansion defines $c(x)$.

Properties

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-The Devil's staircase, also known as the Cantor function, is a function $c \colon [0,1] \rightarrow [0,1]$ can be expressed by the following rules:
+The Devil's staircase (also known as the Cantor function) is a function $c \colon [0,1] \rightarrow [0,1]$ can be expressed by the following rules:
 # Write $x$ in base-3.
 # If that representation of $x$ contains a $1$, replace every digit after the first $1$ with $0$'s.
@@ Line 10: / Line 10: @@
 </gallery>
 </div>
+=Properties=
+[[Devil's staircase is continuous]]<br />
+[[Devil's staircase is not absolutely continuous]]<br />
 =Videos=
-[https://www.youtube.com/watch?v=sjfgim3hrno Cantor's staircase]<br />
+[https://www.youtube.com/watch?v=dQXVn7pFsVI The Devil's Staircase | Infinite Series (19 May 2017)]<br />
+[https://www.youtube.com/watch?v=Hv3fxroMt1s Devil's Staircase (19 February 2017)]<br />
+[https://www.youtube.com/watch?v=TFwiU3W_HoI Intro Real Analysis, Lec 15, Uniform Continuity, Monotone Functions, Devil's Staircase, Derivatives (5 October 2016)]<br />
+[https://www.youtube.com/watch?v=sjfgim3hrno Cantor's staircase (25 November 2014)]<br />
 =References=
-[http://en.wikipedia.org/wiki/Cantor_function Cantor function]
 [[Category:SpecialFunction]]