iésimo

iésimo is a Portuguese ordinal adjective used to indicate the position of an element in a sequence, corresponding to the English term “i-th.” It serves as a generic way to refer to a position when the specific index is variable or not yet specified. The form is typically written as iésimo in masculine singular, iésima in feminine singular, iésimos in masculine plural, and iésimas in feminine plural. In many texts, especially when the index is treated as a variable, it can appear hyphenated as i-ésimo or i-ésima.

In practice, iésimo is prevalent in mathematical, statistical, and computer science contexts. It is used to describe elements of sequences, lists, or arrays: for example, the iésimo termo of a sequence, the iésima posição of a list, or the i-ésimo elemento de um vetor. In formal notation, the iésimo elemento of a sequence is often represented by a_i, emphasizing the indexing by the index i rather than the full word form.

Notes on usage include the common convention in mathematics that indexing often starts at 1 (the first element), while in many programming languages indexing starts at 0. The choice affects how one phrases statements like “for every i-ésimo elemento” or “for i = 1 to n.”

Etymology and related forms are tied to the broader system of ordinal formation in Portuguese, where -ésimo forms are used to ordinalize cardinal concepts and indices. See also ordinal numbers in Portuguese.