Cantor's Intersection Theorem

Author

Eric W. Weisstein
April 14, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Calculus/CantorsIntersectionTheorem.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/CantorsIntersectionTheorem.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Additional Authors

Todd Rowland
Wolfram Research, Inc.

Intersection of intervals [0, t]

This animation shows the intersection of the intervals [0, t] for 0≤ t ≤1.  Cantor's Intersection Theorem is used to show that the Cantor set is nonempty, and may make a more interesting, although confusing, animation.

<<Graphics`Colors`;

movie=Table[Graphics[{Line[{{-1,0},{2,0}}],Purple,PointSize[.03],Thickness[.015],Point[{0,0}],Line[{{0,0},{t,0}}],Point[{t,0}]}],{t,1,0,-.1}];

Show/@movie