Between unequivocal perverty behavior and, say, the light fevered brush-up against somebody's arm on a divan lay a multitude of point-shaving.

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.

Come on, you dog-gone, bullnecked, beetlebrowed, hogjowled, peanutbrained, weaseleyed four flushers, false alarms and excess baggage!

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.