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  title: '"Are all the words in the free group, or just th..."',
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  anchorContext: 'We can use the freely reduced words to construct the free group on a given set $X$; this group has as its elements the words over $X \\cup X^{-1}$, and as its group operation "concatenation followed by free reduction" \\(that is, removal of pairs $r r^{-1}$ and $r^{-1} r$\\)\\.\nThe notion of "freely reduced" basically tells us that $r r^{-1}$ is the identity for every letter $r \\in X$, as is $r^{-1} r$; this cancellation of inverses is a property we very much want out of a group\\.',
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  text: 'Are all the words in the free group, or just the freely-reduced words?\n\nIf the latter, does saying that the group operation involves free reduction imply that only freely-reduced words will end up in the free group? Because, by default I would assume that "the group has as its element the words over $X \\cup X^{-1}$" means that all the words (including non-freely-reduced ones) are in the free group.',
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