Onebased

One-based, or one-based indexing, is the convention of numbering elements of a sequence starting at 1. In this scheme the first element has index 1, the second has index 2, and so on. This contrasts with zero-based indexing, where the first element is at index 0 and the nth element at index n-1.

The term is common in mathematics and in various programming languages and tools that expose user-friendly indexing. Languages such as Fortran, MATLAB, R, Lua, and Mathematica use 1-based indexing for arrays by default. Spreadsheets, databases, and many user interfaces also use 1-based counting for rows and often for columns, making the first data row or column appear at position 1.

Advantages of one-based indexing include alignment with everyday counting and many mathematical formulas, which can reduce off-by-one errors when translating theory to practice. It can also feel more intuitive to non-programmers when selecting data and iterating over sequences.

Disadvantages arise when interfacing with systems that use zero-based indexing. Conversions between schemes can introduce subtle bugs, especially in mixed-language environments or when manipulating memory and pointers in low-level code. In performance-critical software, zero-based indexing is common because it can simplify certain calculations and improve efficiency.

In practice, one-based indexing remains prevalent in mathematical writing and in several high-level languages and tools. Users should be aware of the indexing convention used by their environment to avoid off-by-one errors and to ensure correct data access and interpretation.

See also: zero-based indexing, off-by-one error, arrays, MATLAB, R, Lua, Fortran, spreadsheets.