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→The Free Group
This is called <math>F_2 \ </math>, the free group on two generators. Any group structured like this, in which ''a'' and ''b'' have infinite order and are independent, (ie, no combination of ''a'' and ''b'' form ''e'') is this group. We can picture this group graphically, with ''a'' and ''b'' axes:
This is called <math>F_2 \ </math>, the free group on two generators. Any group structured like this, in which ''a'' and ''b'' have infinite order and are independent, (ie, no combination of ''a'' and ''b'' form ''e'') is this group. We can picture this group graphically, with ''a'' and ''b'' axes:
[[Image:free group.jpg|center|thumb|500px|This depiction demonstrates words of up to four letters; a graphical depiction is [[fractal]] in a fairly obvious fashion.]]
===Paradoxical Decomposition of the Free Group===
===Paradoxical Decomposition of the Free Group===