Come on, you dog-gone, bullnecked, beetlebrowed, hogjowled, peanutbrained, weaseleyed four flushers, false alarms and excess baggage!
Between unequivocal perverty behavior and, say, the light fevered brush-up against somebody's arm on a divan lay a multitude of point-shaving.
Social media companies have been chasing the dream of “social commerce” for years, ramping up advertising and nudging their users toward buying and selling in hopes of getting a piece of the internet’s other most profitable business.
Given a set S of free generators of a free group, let S⁻¹ be the set of inverses of the generators, which are in one-to-one correspondence with the generators (the two sets are disjoint), then let (S∪S⁻¹)* be the Kleene closure of the union of those two sets. For any string w in the Kleene closure let r(w) be its reduced form, obtained by cutting out any occurrences of the form xx⁻¹ or x⁻¹x where x∈S. Noting that r(r(w)) = r(w) for any string w, define an equivalence relation ∼ such that u∼v if and only if r(u)=r(v). Then let the underlying set of the free group generated by S be the quotient set (S∪S⁻¹)*/∼ and let its operator be concatenation followed by reduction.
free generators
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