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→The Free Group
===The Free Group===
===The Free Group===
Before attempting to understand the free group, it would be very beneficial to the reader to have and understanding of a [[Group (mathematics)|mathematical group]].
Let <math>a,a',b,b' \ </math> be "letters." We will form "words" by stringing finitely many of these letters together, subject to just a few simplification rules: <math>aa' = a'a = bb' = b'b= e \ </math>, where <math>e \ </math> is the identity, shorthand for the "word" of zero letters.
===Paradoxical Decomposition of the Free Group===
===Paradoxical Decomposition of the Free Group===