join

Join is a verb meaning to connect two or more things so that they become one, or to become a member of a group or organization. As a noun, a join can refer to a place or method of connection, such as a seam, a pipe joint, or the point where parts are fastened.

In mathematics and logic, join denotes a binary operation that yields the least upper bound of elements within a partially ordered set or lattice. In geometry and algebraic geometry, the join of subspaces is the smallest subspace containing both. The concept is used in lattice theory and related fields to model how elements combine under a given order.

In databases and data processing, a join combines rows from two or more tables according to a related key. SQL supports inner, left, right, and full outer joins, as well as cross joins. A join produces a new relation that includes columns from the joined tables, with match conditions specified in ON or USING clauses.

In crafts, engineering, and construction, a joint refers to the method of connecting parts. Common woodworking joints include butt, lap, mortise-and-tenon, and dovetail joints, while metalworking and plumbing use welded, brazed, or threaded joints to secure components.

Other uses include joining a group or organization, or joining forces in collaboration. The term also appears in phrases describing the act of linking disparate elements or pathways, reflecting its broad sense of connection and union.