1based

1based indexing is a convention in which the first element of an ordered collection is assigned index 1. The term is used in programming, data analysis, and mathematical notation, and is sometimes written as 1based or 1-based.

Languages and systems that use 1based indexing include Fortran, MATLAB, R, Lua, and Julia. In these environments, the first element is referred to as index 1 (for example, a(1) or a[1]), and the last element’s index equals the collection’s length. This aligns with common human counting and many mathematical formulas.

In contrast, many general-purpose programming languages such as C, C++, Java, Python, and JavaScript use 0based indexing, where the first element has index 0. This difference can affect algorithm design, pointer arithmetic, and boundary calculations when porting code between 1based and 0based systems.

Pros and cons exist for each convention. 1based indexing matches everyday counting and traditional mathematical notation, which can reduce certain off-by-one errors in description and documentation. However, it can complicate low-level implementations and require extra adjustments when interfacing with 0based data structures. 0based indexing often simplifies arithmetic involving offsets and array lengths in many languages, but it can increase the potential for off-by-one errors for those more accustomed to counting from 1.

Applications of 1based indexing are common in scientific computing, statistical analysis, and domains where array-like structures are modeled after mathematical sequences. The choice of indexing convention is typically determined by language design and ecosystem conventions.