# Cantor Groups

The Cantor subset of the unit interval $$[0,1)$$ is large in cardinality and also large algebraically, that is, the smallest subgroup of $$[0,1)$$ generated by the Cantor set (using addition mod $$1$$ as the group operation) is the whole of $$[0,1)$$. The authors show how to construct Cantor-like sets which are large in cardinality but small algebraically.

Author(s):
Ben Mathes, Chris Dow, and Leo Livshits
Publication Date:
Tuesday, June 10, 2014
Original Publication Source:
College Mathematics Journal
Original Publication Date:
January, 2011
Subject(s):
Analysis
Real Analysis
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Applicable Course(s):
4.2 Mod Algebra I & II
4.11 Advanced Calc I, II, & Real Analysis
Modify Date:
Tuesday, June 10, 2014