negativeindex

Negative indexing, or a negative index, is a convention in some programming languages and mathematical contexts where an index value can be negative to refer to elements from the end of a sequence rather than from the start. In languages that support it, a negative index provides a convenient way to access elements without computing the sequence length. For example, in a list of length n, an index of -1 refers to the last element, -2 to the second last, and so on.

In programming, negative indexing is commonly associated with languages such as Python and Ruby. In Python, for instance, a[-1] returns the last element, and a[-n] returns the nth element from the end. Access to negative indices is typically bounds-checked, and indices beyond the valid range raise an error. Other languages may implement negative indexing differently or not at all; some treat negative indices as invalid or as ordinary string keys rather than array positions. JavaScript, for example, does not support negative indices as array positions, though it can treat a property like arr[-1] as a non-indexed property.

In mathematics and related fields, indexing by negative integers is also used in discussions of bilateral sequences and Laurent series, where indices can extend to negative values. This broader usage is not tied to a specific programming language but reflects a way to index objects indexed by the set of all integers.

Practical considerations include ensuring language-specific behavior is understood, validating indices, and being mindful of portability when writing code or algorithms that rely on negative indexing.