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Dumb question: The first sentence is ```In group theory, a word is any written product of group elements and their inverses.``` Don't a group's elements always include all inverses? Acorn (Nathan) (talk) 15:47, 13 October 2021 (UTC)[reply]
The article is not explicit on this, but a word is some particular kind of formal expression (called term in logic and theoretical computer science; I guess group words were investigated before the introduction of computers and formal languages, and hence use a different terminology). As a more familiar analogy, a polynomial is something similar, and while both x3+1 and x5+1 may evaluate to any real number (if x is substituted appropriately), they are quite different as polynomials. Group words are used in Presentation of a group, and the section Examples there includes words with negative exponents. - Jochen Burghardt (talk) 17:25, 13 October 2021 (UTC)[reply]
