In Computer Programming
This usage follows from design choices embedded in many influential programming languages, including C, Java, and Lisp. In these three, sequence types (C arrays, Java arrays and lists, and Lisp lists and vectors) are indexed beginning with the zero subscript. Particularly in C, where arrays are closely tied to pointer arithmetic, this makes for a simpler implementation: the subscript refers to an offset from the starting position of an array, so the first element has an offset of zero.
Referencing memory by an address and an offset is represented directly in computer hardware on virtually all computer architectures, so this design detail in C makes compilation easier, at the cost of some human factors. In this context using "zeroth" as an ordinal is not strictly correct, but professional shorthand. Older programming languages, such as Fortran or Cobol have array subscripts starting with one, because they were meant as high-level programming languages, and as such they had to have a correspondence to the usual ordinal numbers. Some recent languages, such as Lua, have adopted the same convention for the same reason.
Zero is the lowest unsigned integer value, one of the most fundamental types in programming and hardware design. In computer science, zero is thus often used as the base case for many kinds of numerical recursion. Proofs and other sorts of mathematical reasoning in computer science often begin with zero. For these reasons, in computer science it is not unusual to number from zero rather than one.
Hackers and computer scientists often like to call the first chapter of a publication "Chapter 0", especially if it is of an introductory nature. One of the classic instances was in the First Edition of K&R. In recent years this trait has also been observed among many pure mathematicians, where many constructions are defined to be numbered from 0.
If an array is used to represent a cycle, it is convenient to obtain the index with a modulo operator, which can result in zero.
Read more about this topic: Zero-based Numbering
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