zeroindexing

Zero-indexing is a convention in computer programming and mathematics where the first element of a sequence or array is assigned the index 0. This is in contrast to one-indexing, where the first element is assigned the index 1. Many programming languages, including C, C++, Java, Python, and JavaScript, use zero-indexing for their arrays and strings. This choice has implications for how data structures are accessed and manipulated.

The origin of zero-indexing is often attributed to the early design decisions in the FORTRAN programming language and later cemented by the influential language C. One reason for its adoption is its compatibility with the underlying hardware architecture of computers, which often uses memory addresses that start from zero. This can lead to simpler and more efficient implementations of array access.

When working with zero-indexed sequences, it's important to be mindful of the index range. For a sequence of length N, the valid indices will range from 0 to N-1. Attempting to access an element at index N or beyond, or at a negative index, will typically result in an error, such as an "index out of bounds" exception. This convention can sometimes lead to off-by-one errors if programmers are not accustomed to it, especially when translating algorithms from one indexing system to another. While some languages and mathematical contexts use one-indexing, zero-indexing remains a prevalent and fundamental concept in modern computing.