residuum

Residuum is a term with multiple senses across disciplines, all connected by the notion of what remains after a process. In chemistry and related fields, residuum (also residue) denotes the material left behind after purification, distillation, filtration, or extraction. It may contain impurities and often undergoes further treatment to extract usable components or to dispose of waste. The term is common in older or technical literature; in modern usage, "residue" is more typical, but residuum is still encountered in petroleum refining, mineral processing, and pharmacognosy to describe heavy fractions or solids left after processing.

In mathematics, residuum refers to a residual operation associated with a binary operation in a lattice or ordered algebra. When a monoidal product ⊗ is defined on a poset, the residuum (or residual) is the greatest element c such that a ⊗ c ≤ b. The residuation property yields an adjunction: a ⊗ c ≤ b if and only if c ≤ a ⇒ b. This residuum operation is central to residuated lattices and provides a formal notion of implication used in substructural and fuzzy logics.

Originating from Latin residuum meaning remainder, residuum is etymologically related to residue. The terms residuum, residua, and residues are related but have domain-specific connotations; residuum tends to appear in technical or mathematical contexts, while residue is common in everyday language and many sciences.