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-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 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 w

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  • 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-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 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. (en)
  • オリジン(origin)とは、原点のことで、主に0オリジンと1オリジンが存在する。0オリジンのものは0から数え始め、1オリジンのものは1から数え始める。ちなみに0オリジンと1オリジンは和製英語で、英語ではzero-basedとone-basedなどという。 (ja)
  • Nollte är det ordningstal som motsvarar grundtalet noll. Begreppet "nollte" används bland annat när man i efterhand lagt till något i början av en numrerad lista och är i svenska språket dokumenterat sedan 1924. Med ordningstalet nollte, eller index noll, blir punkt fem den sjätte punkten vilket kan upplevas ologiskt. Det följer emellertid samma princip som uttrycket ”fem år gammal, på det sjätte”. (sv)
  • 從0開始編號或索引開頭為0是一種編號方式,在序列其中初始元素的索引被分配到的數字是零,而非一般日常環境中典型的索引開頭為一。從零開始的編號方式,序列中初始的元素有時被稱為第零元素(一般稱為第一元素);「第零」索引是對應於數字零的序數。 某些情況下,原來並不屬於該序列的物件或值,但可以自然地放置在其初始元素之前的,或稱其為第零元素。使用零作為序數並未被廣泛接受,因為在缺乏上下文時,對序列的所有後續元素會造成混淆。 從0開始編號的序列在數學符號中是相當常見的,特別是在組合數學中,儘管數學領域的編程語言通常從一開始編號。計算機科學中,現代編程語言中(例如C語言)陣列的索引通常從0開始,因此編程人員會用「第零」開始索引,而其他人是使用「第一」開始索引的情況。在數學中對於出現在「第一個」之前的元素,其序數形式有明確的定義時,則使用從零開始的編號不會造成混淆;例如函數的第零階導數是進行零次微分獲得的,亦即函數本身。對應於不屬於該序列,但以這樣子命名法在其之前面的元素,或不妥當:所謂「第零階」的導數實際並非導數。然而,正如一階導數在二階導數之前,因此第零階導數(或原始函數本身)也在一階導數之前。 (zh)
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  • オリジン(origin)とは、原点のことで、主に0オリジンと1オリジンが存在する。0オリジンのものは0から数え始め、1オリジンのものは1から数え始める。ちなみに0オリジンと1オリジンは和製英語で、英語ではzero-basedとone-basedなどという。 (ja)
  • Nollte är det ordningstal som motsvarar grundtalet noll. Begreppet "nollte" används bland annat när man i efterhand lagt till något i början av en numrerad lista och är i svenska språket dokumenterat sedan 1924. Med ordningstalet nollte, eller index noll, blir punkt fem den sjätte punkten vilket kan upplevas ologiskt. Det följer emellertid samma princip som uttrycket ”fem år gammal, på det sjätte”. (sv)
  • 從0開始編號或索引開頭為0是一種編號方式,在序列其中初始元素的索引被分配到的數字是零,而非一般日常環境中典型的索引開頭為一。從零開始的編號方式,序列中初始的元素有時被稱為第零元素(一般稱為第一元素);「第零」索引是對應於數字零的序數。 某些情況下,原來並不屬於該序列的物件或值,但可以自然地放置在其初始元素之前的,或稱其為第零元素。使用零作為序數並未被廣泛接受,因為在缺乏上下文時,對序列的所有後續元素會造成混淆。 從0開始編號的序列在數學符號中是相當常見的,特別是在組合數學中,儘管數學領域的編程語言通常從一開始編號。計算機科學中,現代編程語言中(例如C語言)陣列的索引通常從0開始,因此編程人員會用「第零」開始索引,而其他人是使用「第一」開始索引的情況。在數學中對於出現在「第一個」之前的元素,其序數形式有明確的定義時,則使用從零開始的編號不會造成混淆;例如函數的第零階導數是進行零次微分獲得的,亦即函數本身。對應於不屬於該序列,但以這樣子命名法在其之前面的元素,或不妥當:所謂「第零階」的導數實際並非導數。然而,正如一階導數在二階導數之前,因此第零階導數(或原始函數本身)也在一階導數之前。 (zh)
  • 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-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 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 w (en)
rdfs:label
  • Zero-based numbering (en)
  • オリジン (ja)
  • Nollte (sv)
  • 從零開始的編號 (zh)
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