Jth

Jth, typically written as j-th (or less commonly as jth), is a notation used to denote the j-th item in a sequence, where j is an integer index. It functions as a positional indicator rather than a word with its own meaning, and it appears across mathematics, computer science, and related fields.

In mathematics, j is a running index used to refer to elements of sequences, functions, or indexed families. For a sequence {a_j}, the j-th term is a_j. In proofs, summations, and limits, indices like j help track individual elements within a broader collection, such as a_j, f(j), or X_j.

In computer science and programming, j commonly appears as a loop index or as a coordinate in arrays, lists, or matrices. For example, in a loop such as for j from 1 to n, the j-th element of an array A is referenced as A_j (or A[j] in code). In zero-based indexing languages, the j-th element typically corresponds to A[j], with j ranging from 0 to n-1.

Orthography and style: most guides prefer the hyphenated form j-th (to avoid misreading as a single word). Some texts may use jth or similar variants, but consistency within a document is advised.

See also: index notation, indexing, sequences, multi-index notation.