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). In Mathematics, a natural number (also called counting number) can mean either an element of the set (the positive Integers or an
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. In Computer science an array is a Data structure consisting of a group of elements that are accessed by indexing. A computer is a Machine that manipulates data according to a list of instructions. See also Hacker In home computing a hacker is a person who heavily modifies the software or hardware of their computer system Computer science (or computing science) is the study and the Science of the theoretical foundations of Information and Computation and their The word geek is a Slang term noting individuals as "a peculiar or otherwise odd person especially one who is perceived to be overly obsessed with one or more things 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.
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In computer programming
This usage follows from design choices embedded in many influential programming languages, including C, Java, and Lisp. A programming language is an Artificial language that can be used to write programs which control the behavior of a machine particularly a Computer. tags please moot on the talk page first! --> In Computing, C is a general-purpose cross-platform block structured Lisp (or LISP) is a family of Computer Programming languages with a long history and a distinctive fully parenthesized syntax 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 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. In Set theory, an ordinal number, or just ordinal, is the Order type of a Well-ordered set.
Zero is the lowest unsigned integer value, one of the most fundamental types in programming and hardware design. Hardware is a general term that refers to the physical artifacts of a Technology. In computer science, zero is thus often used as the base case for many kinds of numerical recursion. Recursion, in Mathematics and Computer science, is a method of defining functions in which the function being defined is applied within its own definition 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. The C Programming Language (sometimes referred to as K&R or the white book) is a well-known Computer science Book In recent years this trait has also been observed among many pure mathematicians, where many constructions are defined to be numbered from 0. Broadly speaking pure mathematics is Mathematics motivated entirely for reasons other than application
Zero-based numbering tends to reduce fencepost errors, though it cannot eliminate them entirely, and may even introduce them in a few cases. An off-by-one error (OBOE is a logical error involving the discrete equivalent of a Boundary condition.
Other than computing
In mathematics, many sequences of numbers or of polynomials are indexed by nonnegative integers, for example the Bernoulli numbers and the Bell numbers. Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and In Mathematics, a polynomial is an expression constructed from Variables (also known as indeterminates and Constants using the operations In Mathematics, the Bernoulli numbers are a Sequence of Rational numbers with deep connections to Number theory. In combinatorial Mathematics, the n th Bell number, named in honor of Eric Temple Bell, is the number of partitions of a set
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. The zeroth law of thermodynamics is a generalized statement about thermal Equilibrium between bodies in contact
In the realm of fiction, Isaac Asimov eventually added a Zeroth Law to his famous Three Laws of Robotics, essentially making them four laws. Isaac Asimov (c January 2 1920 &ndash April 6 1992 ˈaɪzək ˈæzɪmʌv originally Исаак Озимов but now transcribed into Russian as, was a Russian In Science fiction, the Three Laws of Robotics are a set of three rules written by Isaac Asimov, which almost all positronic robots appearing in his fiction
Some buildings in the British English speaking world refer to the ground floor as floor 0. British English or UK English ( BrE, BE, en-GB) is the broad term used to distinguish the forms of the English language used in the A storey (spelled story in the USA only floor, deck or level is the level of a Building above (or below the Ground.
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". Anton Bruckner (4 September 1824 &ndash 11 October 1896 was an Austrian composer known primarily for his symphonies, masses, and Motets 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. This Symphony in D minor composed by Anton Bruckner was not assigned a number by its composer and has subsequently become known by the German designation Die Nullte Anton Bruckner 's Symphony No 1 in C minor was the first symphony the composer thought worthy of performing and bequeathing to the Vienna national library There's an even earlier Symphony in F minor of Bruckner's that is sometimes called No. 00. Anton Bruckner 's Study Symphony in F minor, ( Studiensymphonie) or simply Symphony in F minor, WAB 99 was written in 1863 as an exercise under Otto Kitzler's
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". Orientation week is the first week of the academic year at a University or other tertiary institution and a variety of events are held to help orient and welcome As a parallel, the introductory weeks at university educations in Sweden are generally called "nollning" (zeroing). "Sverige" redirects here For other uses see Sweden (disambiguation and Sverige (disambiguation.
Since the United States Air Force starts basic training each Wednesday, trainees are left with four days before the first week of the eight-week training starts. These four days are often referred to as "Zero Week. "
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).
In Uppsala and Cardiff the train stations have a platform 0. Uppsala ˈɵpˌsɑːla (older spelling Upsala) is the capital of Uppsala County ( Uppsala län) and the fourth largest city of Cardiff Central railway station (Caerdydd Canolog is a major British railway station on Central Square in Cardiff, Wales.
See also
- Orders of approximation for "Zeroth-order approximation". Orders of approximation have been used not only in Science, Engineering, and other quantitative disciplines to make Approximations with various degrees
- Zero hour
References
This article was originally based on material from the Free On-line Dictionary of Computing, which is licensed under the GFDL. The Free On-line Dictionary of Computing ( FOLDOC) is an online searchable encyclopedic Dictionary of Computing subjects The GNU Free Documentation License ( GNU FDL or simply GFDL) is a Copyleft License for free documentation designed by the Free Software
Dictionary
zeroth
-adjective
- (mathematics): In the first position in a sequence whose elements are numbered starting at zero; the ordinal number corresponding to zero.
- Corresponding to a position preceding the first.
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