joining

Joining is the act or process of bringing two or more elements together to form a single, coherent entity. It can refer to physical connections, mathematical operations, or social processes that unify separate components.

In mathematics and logic, joining denotes the operation of combining elements to form their least upper bound in a lattice, often called the join. The join of two elements is the smallest element that is greater than or equal to both. In set theory, related concepts include unions, which combine all elements from each set. In database and information theory, joins connect data from different sources based on related attributes.

In databases, a join is a binary operation that merges rows from two or more tables by matching common attributes. Types include inner join (returns only matching rows), left or right outer joins (include non-matching rows from one side), full outer join (includes all rows), and cross join (cartesian product). Joins enable relational queries to combine related data without duplicating information.

Physically joining parts involves methods such as welding, soldering, riveting, brazing, gluing, or mechanical fasteners. Joint design considers material compatibility, load paths, durability, environmental exposure, and desired strength. In woodworking and metalworking, common joints include butt, mortise-and-tenon, dovetail, lap, and scarf joints, each balancing strength, alignment, and ease of fabrication.

Socially, joining a group or organization entails membership, onboarding, and participation. This aspect emphasizes integration, shared norms, and collaborative activity within a community. See also: union, merge, connect.