Where does union collide?

In the algebra of classes that George Boole set out in 1854 in An Investigation of the Laws of Thought, the union of two classes is the operation Boole called logical addition: it forms the single class holding everything that belongs to either one. Georg Cantor's 1895 Beiträge zur Begründung der transfiniten Mengenlehre carried the same idea into set theory, where the union of a collection of sets is the set of all elements that lie in at least one of them. Here the referent is a defined operation on collections of objects, governed by axioms and written with the symbol ∪. It has nothing in common with an association of workers or the knitting of a broken bone.[1][2]

Unit

One operation on sets: given two or more sets, it returns the set of all their members combined, counting each once

Recovery means

Not applicable

Measured by

Defined by axiom rather than measured; the number of members in a finite union follows from adding the sets and subtracting their overlap

Sidney and Beatrice Webb, in their 1894 The History of Trade Unionism, defined a trade union as a continuous association of wage earners formed to maintain or improve the conditions of their working lives. Such a body bargains collectively with employers over pay, hours, and working conditions, and represents its members in disputes. Freeman and Medoff's 1984 What Do Unions Do? gave the modern economic account of how unions affect wages, worker turnover, and productivity. Here the referent is an organized body of workers acting together, not an operation on sets or the mending of a fractured bone.[3][4]

Unit

One organized association of workers, bounded by its membership and its recognized bargaining scope

Recovery means

Not applicable

Measured by

Counted by membership numbers and union density, the share of workers who belong, and studied through collective bargaining agreements and their wage effects

In orthopedic medicine, union is the healing by which the fragments of a broken bone consolidate back into one continuous, load-bearing structure. Thomas Einhorn's 1998 review The Cell and Molecular Biology of Fracture Healing described the stages by which a fracture bridges, from the early blood clot and inflammation through a soft callus to mineralized bone. When this process stalls the result is a nonunion, and when the bone heals in a poor position it is a malunion. Here the referent is a biological repair inside a living body, and it is unrelated to a union of sets or an association of workers.[5]

Unit

One healed fracture: restored bony continuity across a single break

Recovery means

The callus remodels over months as woven bone is gradually replaced by stronger layered bone

Measured by

Judged clinically and on radiographs by bridging callus and the absence of motion at the fracture line; failure is graded as delayed union or nonunion