ith

The term ith refers to the position of an element within an ordered sequence, typically expressed as the i-th element where i denotes an index. It is formed by combining the variable i with the ordinal suffix used in English. In mathematical and computer science contexts, i is a stand-in for an integer index, so the phrase “the ith element” or “the i-th term” points to the element at position i in a list, array, or sequence.

Usage and conventions vary by field and style guide. In many technical texts, the preferred notation is i-th with a hyphen (i-th) to clarify pronunciation and avoid ambiguity. Some prose writers with different conventions may render it as ith in running text, but hyphenation is common in formal writing. The letter i is commonly used as an index and may range over natural numbers starting at 0 or 1, depending on the convention being adopted.

In programming, i-th elements appear frequently in loops and algorithms. Examples include iterating over an array with a loop like for i from 0 to n-1, processing the i-th entry. In pure mathematics, i often serves as a dummy index in sequences and sums, indexing terms by i.

The concept is distinct from other ordinal forms such as third or fifth, which arise from irregular English morphologies. The i-th form explicitly signals a position determined by an index, rather than relying on the fixed word-based ordinals. See also indexing, ordinal indicators, and zero- or one-based indexing.