Dellinsieme

Dell’insieme, written dell’insieme in Italian, is the contracted prepositional phrase meaning “of the set.” It is used in mathematical and logical writing to indicate a relation of belonging or attribution to a specific set. The form is formed from di (“of”) plus l’insieme (“the set”), with elision producing dell’insieme before a vowel.

Common usages include phrases such as elementi dell’insieme A (elements of the set A), un elemento dell’insieme X (an element of the set X), sottoinsieme dell’insieme B (a subset of the set B), and proprietà dell’insieme C (properties of the set C). In these constructions, dell’insieme functions as a connector that ties a property, element, or subset to the referenced set.

Grammatically, dell’insieme is not a standalone mathematical object; it is a relational phrase. It appears in Italian mathematical prose to specify that a statement concerns a particular set, and it is commonly found in definitions, explanations, and descriptions of set-related concepts.

Etymology and usage notes: insieme is the Italian word for “set” or “collection,” derived from the sense of bringing things together. The article l’ before insieme becomes dell’ in this prepositional form, reflecting standard Italian syntax di + l’insieme → dell’insieme.

See also: Set (mathematics), Subset, Element (set theory), Italian language.