Definition
Let G be a group, and let S be a subset of G. A word in S is any expression of the form
where s1,...,sn are elements of S and each εi is ±1. The number n is known as the length of the word.
Each word in S represents an element of G, namely the product of the expression. By convention, the identity element can be represented by the empty word, which is the unique word of length zero.
Read more about this topic: Word (group Theory)
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“Beauty, like all other qualities presented to human experience, is relative; and the definition of it becomes unmeaning and useless in proportion to its abstractness. To define beauty not in the most abstract, but in the most concrete terms possible, not to find a universal formula for it, but the formula which expresses most adequately this or that special manifestation of it, is the aim of the true student of aesthetics.”
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—Ralph Waldo Emerson (1803–1882)