Generalized Unions and Intersections of Empty Sets From USgf{xI3T∈S.xeT} ∩Sg{x|TeS.xeT} we know U0=0 ∩0 meaningless 0is meaningless,since it denotes the paradoxical "set of everything". 9/40Generalized Unions and Intersections of Empty Sets From S S def = {x | ∃T ∈ S. x ∈ T} T S def = {x | ∀T ∈ S. x ∈ T} we know S ∅ = ∅ T ∅ meaningless T ∅ is meaningless, since it denotes the paradoxical ”set of everything”. 9 / 40