Vn

Vn, written as V with a subscript n, is a common notation in mathematics, physics, electrical engineering, and related fields. The variable n is typically an integer index representing order, a time step, a position in a sequence, or a labeling of components. Because many disciplines adopt the same symbol for different concepts, the precise meaning of Vn must be inferred from context and the definitions provided in a given text.

In mathematics, Vn often denotes the nth term of a sequence, such as a_n or b_n, or the nth object in a family indexed by n. In linear algebra and topology, V0 ⊆ V1 ⊆ ... can denote a filtration of vector spaces, with Vn representing the subspace at stage n. In graph theory, V typically denotes the vertex set; Vn may be used to label a sequence of graphs or to denote the vertex set of a particular graph Gn when indexing by n.

In physics and electrical engineering, Vn frequently labels a node voltage or a reference/supply rail that is indexed by n, for example for multiple power rails or measurement points (V1, V2, …). In signal processing, Vn might denote the nth sample of a voltage signal. In numerical methods, Vn can reference a provisional solution at the nth iteration.

Notational differences are common: many authors use lowercase v_n for a vector (v_n) rather than an entire space V_n, and reserve uppercase V for a vector space, a set, or a function class. Always consult the definitions in the source material to avoid ambiguity.