Donis Marshall

Zero-based numbering is a way of numbering in which the initial element of a sequence is assigned the index 0, rather than the index 1 as is typical in everyday non-mathematical or non-programming circumstances. Under zero-based numbering, the initial element is sometimes termed the zeroth element, rather than the first element; zeroth is a coined word for the ordinal number zero. In some cases, an object or value that does not (originally) belong to a given sequence, but which could be naturally placed before its initial element, may be termed the zeroth element. There is no wide agreement regarding the correctness of using zero as an ordinal (nor regarding the use of the term zeroth), as it creates ambiguity for all subsequent elements of the sequence when lacking context.
Numbering sequences starting at 0 is quite common in mathematics notation, in particular in combinatorics, though programming languages for mathematics usually index from 1.