Zeroth

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The zeroth item is the initial item of a zero-based sequence (that is, a sequence which is numbered beginning from zero rather than one), such as the non-negative integers (see natural number).

This kind of numbering is common in array references in computer systems, so hackers, computer scientists and computer geeks often use zeroth where others might use first, and so forth. Although there is logical reasoning for this (explained below) in programming and mathematics, there is little logical^[1] reasoning to use this in other areas, yet it often is.

1 In computer programming
2 Besides computing
3 See also
4 References

[edit] 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. In reality, the subscript refers to an offset from the starting position of an array. Therefore, the first element would have an offset of zero.

Referencing memory by an address and an offset is represented directly in hardware on virtually all computer architectures, so this design detail in C makes compilation easier and run times faster, at the cost of some human factors. In this context using "zeroth" as an ordinal is not strictly correct, but professional shorthand. Other higher-level languages have adopted array subscripts starting with one for a closer correspondence to the usual ordinal numbers.

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.

Zero-based numbering tends to reduce fencepost errors, though it cannot eliminate them entirely, and may even introduce them in a few cases.

[edit] Besides computing

In mathematics, many sequences of numbers or of polynomials are indexed by nonnegative integers, for example the Bernoulli numbers and the Bell numbers.

A common use of zeroth outside computing is in the name of the zeroth law of thermodynamics, a law that was formulated after the first, second and third laws, but considered more fundamental.

In the realm of fiction, Isaac Asimov eventually added a Zeroth Law to his famous Three Laws of Robotics, essentially making it a four laws of robotics

Some buildings in the British English speaking world refer to the ground floor as floor 0, which may be confusing for speakers of American English.

While the ordinal of 0 is rarely used outside of communities closely connected to mathematics, physics, and computer science, there is one instance of it in classical music. The composer Anton Bruckner regarded his early Symphony in D minor to be unworthy of including in the canon of his works, and he wrote 'gilt nicht' on the score and a circle with a crossbar, intending it to mean "invalid". But posthumously, this work came to be known as Symphony No. 0 in D minor, even though it was actually written after Symphony No. 1 in C minor. There's an even earlier Symphony in F minor of Bruckner's that is sometimes called No. 00.

In biological or medical experiments, initial measurements made before any experimental time has passed are said to be on the 0 day of the experiment.

In some universities, including Oxford and Cambridge, "week 0" or occasionally "noughth week" refers to the week before the first week of lectures in a term. In Australia, some universities refer to this as "O Week", which serves as a pun on "Orientation week". As a parallel, the introductory weeks at university educations in Sweden are generally called "nollning" (zeroing).

Note also the use of 00 hours in the 24-hour clock as beginning of the day, although this is most likely a result of ensuring the conversion from 12-hour to 24-hour format is as simple as possible. To convert from one time format to another, simply add or subtract 12 from the hour for a PM time, whilst an AM time is identical in both formats. If the 24 hour clock started from hour 01, then this would make this calculation slightly more complicated (subtract/add 13 from the hour for a PM time, and subtract/add 1 from the hour for an AM time).