inseparable

Inseparable is an adjective used to describe things or people that cannot be separated or easily divided, either physically or figuratively. It is commonly employed to express a strong bond, close association, or mutual dependence between entities such as individuals, objects, or ideas.

The term derives from the combination of in- (not) and separable, itself from Latin separabilis, meaning capable of being separated. In everyday language, it often conveys a sense of enduring connection or unity, as in inseparable friends or inseparable teams.

In mathematics, inseparability has a specialized meaning in field theory. An algebraic field extension L/K is called inseparable if some element of L is a root of a polynomial with coefficients in K that has repeated roots, a situation that can occur only in positive characteristic. A purely inseparable or inseparable extension is one where every element of L is a root of a polynomial of the form X^{p^n} − a with p the characteristic of K.

In culture, the term Inseparable has been used as a title or motif in various works of art, including films, literature, and music, often to emphasize themes of unity, loyalty, or an unbreakable bond. Regardless of usage, the core sense remains the same: the subjects are bound together beyond ordinary separation.

See also: inseparability.