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• Zero-based_numbering abstract "Zero-based numbering or index origin = 0 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-programming circumstances. Under zero-based numbering, the initial element is sometimes termed the zeroth element, rather than the first element; zeroth is a coined ordinal number corresponding to the 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 not 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. In computer science, array indices usually start at 0 in modern programming languages, so computer programmers might use zeroth in situations where others might use first, and so forth. In some mathematical contexts, zero-based numbering can be used without confusion, when ordinal forms have well established meaning with an obvious candidate to come before first; for instance a zeroth derivative of a function is the function itself, obtained by differentiating zero times. Such usage corresponds to naming an element not properly belonging to the sequence but preceding it: the zeroth derivative is not really a derivative at all. However, just as the first derivative precedes the second derivative, so also does the zeroth derivative (or the original function itself) precede the first derivative.".
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• Zero-based_numbering wikiPageRevisionID "706936429".
• Zero-based_numbering wikiPageWikiLink 0_(number).
• Zero-based_numbering wikiPageWikiLink 0_(year).
• Zero-based_numbering wikiPageWikiLink 1.
• Zero-based_numbering wikiPageWikiLink 1_BC.
• Zero-based_numbering wikiPageWikiLink 24-hour_clock.
• Zero-based_numbering wikiPageWikiLink Alfred_Schnittke.
• Zero-based_numbering wikiPageWikiLink Anton_Bruckner.
• Zero-based_numbering wikiPageWikiLink Antwerp.
• Zero-based_numbering wikiPageWikiLink Array_data_structure.
• Zero-based_numbering wikiPageWikiLink Astronomical_year_numbering.
• Zero-based_numbering wikiPageWikiLink BCPL.
• Zero-based_numbering wikiPageWikiLink Bell_number.
• Zero-based_numbering wikiPageWikiLink Bernoulli_number.
• Zero-based_numbering wikiPageWikiLink Brussels.
• Zero-based_numbering wikiPageWikiLink Buddhist_calendar.
• Zero-based_numbering wikiPageWikiLink COBOL.
• Zero-based_numbering wikiPageWikiLink C_(programming_language).
• Zero-based_numbering wikiPageWikiLink Cardiff_Central_railway_station.
• Zero-based_numbering wikiPageWikiLink Category:0_(number).
• Zero-based_numbering wikiPageWikiLink Category:Ordinal_numbers.
• Zero-based_numbering wikiPageWikiLink Combinatorics.
• Zero-based_numbering wikiPageWikiLink Computer_hardware.
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• Zero-based_numbering wikiPageWikiLink Dereference_operator.
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• Zero-based_numbering wikiPageWikiLink Epidemiology.
• Zero-based_numbering wikiPageWikiLink Fortran.
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• Zero-based_numbering wikiPageWikiLink High-level_programming_language.
• Zero-based_numbering wikiPageWikiLink Hindu_calendar.
• Zero-based_numbering wikiPageWikiLink IBM.
• Zero-based_numbering wikiPageWikiLink IBM_7090.
• Zero-based_numbering wikiPageWikiLink ISO_8601.
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• Zero-based_numbering wikiPageWikiLink Indexed_family.
• Zero-based_numbering wikiPageWikiLink Interval_(mathematics).
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• Zero-based_numbering wikiPageWikiLink Java_(programming_language).
• Zero-based_numbering wikiPageWikiLink Julian_calendar.
• Zero-based_numbering wikiPageWikiLink Lisp_(programming_language).
• Zero-based_numbering wikiPageWikiLink London_Kings_Cross_railway_station.
• Zero-based_numbering wikiPageWikiLink Lua_(programming_language).
• Zero-based_numbering wikiPageWikiLink Martin_Richards_(computer_scientist).
• Zero-based_numbering wikiPageWikiLink Mathematics.
• Zero-based_numbering wikiPageWikiLink Memory_address.
• Zero-based_numbering wikiPageWikiLink Modular_arithmetic.
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• Zero-based_numbering wikiPageWikiLink Off-by-one_error.
• Zero-based_numbering wikiPageWikiLink Order_of_approximation.
• Zero-based_numbering wikiPageWikiLink Ordinal_number_(linguistics).
• Zero-based_numbering wikiPageWikiLink Patient.
• Zero-based_numbering wikiPageWikiLink Pointer_(computer_programming).
• Zero-based_numbering wikiPageWikiLink Polynomial.
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• Zero-based_numbering wikiPageWikiLink Robert_Crumb.
• Zero-based_numbering wikiPageWikiLink Run_time_(program_lifecycle_phase).
• Zero-based_numbering wikiPageWikiLink SBB-CFF-FFS_Re_460.
• Zero-based_numbering wikiPageWikiLink Sample_(statistics).
• Zero-based_numbering wikiPageWikiLink Sequence.
• Zero-based_numbering wikiPageWikiLink Stockport_railway_station.
• Zero-based_numbering wikiPageWikiLink Storey.
• Zero-based_numbering wikiPageWikiLink Student_orientation.
• Zero-based_numbering wikiPageWikiLink Study_Symphony_in_F_minor.
• Zero-based_numbering wikiPageWikiLink Sweden.
• Zero-based_numbering wikiPageWikiLink Swiss_Federal_Railways.
• Zero-based_numbering wikiPageWikiLink Symphony_No._1_(Bruckner).
• Zero-based_numbering wikiPageWikiLink Symphony_in_D_minor_(Bruckner).
• Zero-based_numbering wikiPageWikiLink The_C_Programming_Language.
• Zero-based_numbering wikiPageWikiLink Three_Laws_of_Robotics.
• Zero-based_numbering wikiPageWikiLink United_States_Air_Force.
• Zero-based_numbering wikiPageWikiLink Uppsala.
• Zero-based_numbering wikiPageWikiLink Velocity_prediction_program.
• Zero-based_numbering wikiPageWikiLink Yonago,_Tottori.
• Zero-based_numbering wikiPageWikiLink Zap_Comix.
• Zero-based_numbering wikiPageWikiLink Zeroth_law_of_thermodynamics.
• Zero-based_numbering wikiPageWikiLink Zork_Zero.
• Zero-based_numbering wikiPageWikiLinkText "0-based".
• Zero-based_numbering wikiPageWikiLinkText "Index Origin".
• Zero-based_numbering wikiPageWikiLinkText "Zero-based numbering".
• Zero-based_numbering wikiPageWikiLinkText "Zero-based numbering#OFFSET".
• Zero-based_numbering wikiPageWikiLinkText "Zero-based_numbering".
• Zero-based_numbering wikiPageWikiLinkText "Zeroth".
• Zero-based_numbering wikiPageWikiLinkText "counting from '''zero'''".
• Zero-based_numbering wikiPageWikiLinkText "counting from zero".
• Zero-based_numbering wikiPageWikiLinkText "counting starts with zero".
• Zero-based_numbering wikiPageWikiLinkText "index origin".

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