Talk:Zero-based numbering

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Alternative terms[edit]

Apart from being horrible English, aren't there already alternatives? Isn't "nought" used in this way? --MacRusgail 14:48, 6 February 2006 (UTC)

"The nought element, the first element, the second element"... ? No, I don't think it is. Zeroth is a term which fills a need in math and computer science, as silly as it may sound to those who aren't in those fields. --FOo 17:39, 6 February 2006 (UTC)

Irrelevant examples[edit]

I would say that at least half of the examples in the "Other than computing" section are irrelevant. That an item merely is identified by the number zero doesn't automatically mean that people refer to it as the zeroth item. 00:00:00 is the moment when the 24th hour ends and the 1st begins, but it is certainly not in any sense belonging to a "zeroth hour". And I'm fairly certain that nobody in Uppsala or Cardiff ever talks about the zeroth track, only about track zero. Such a factoid could be relevant in an article about zero, but not in an article about zeroth.

And even those examples that might be relevant should really be sourced. The zeroth floor? Bruckner's zeroth (or even double-zeroth) symphony? Does someone say this? Are there reliable sources? This article is not merely about things labeled with the number zero. -- Jao 12:37, 23 August 2007 (UTC)

I agree. Clocks show cardinal numbers, not ordinal. With time displayed by clocks, 00:01:57 refers to time elapsed since midnight and not the current hour. When clock displays 00:01:57 we are in fact in the first hour of the day, while 23:01:57 means we're in the 24th. There is no zeroth hour. Waydot (talk) 22:34, 30 October 2008 (UTC)
OK so I did the bold thing and deleted all the "examples" that don't explicitly specify the ordinal "Zeroth". Roger (talk) 20:42, 7 April 2010 (UTC)
So is the article about a word rather than a concept? —Tamfang (talk) 16:16, 8 April 2010 (UTC)
This article is about Zero as an Ordinal number. Roger (talk) 16:03, 9 April 2010 (UTC)
Of which "Symphony No. 0" is a cromulent example, whether or not the exact word zeroth is used. —Tamfang (talk) 03:59, 10 April 2010 (UTC)
First, I think Roger meant to point to Ordinal number (linguistics). And no, in "Symphony No. 0" the "0" is not linguistically an ordinal number (it is no adjective for instance). It has the form of a cardinal number (linguistics), but is not used to represent a quantity either; it is just a label, which could be in principle any string, as in "version 4.5.17.a". Second, why restrict to "Other than computing"? I see that the "In computer programming" section hardly addresses the notion of "zeroth" at all either. So I would propose to (1) restore the contents removed, (2) rename this article to "Zero based indexing", and (3) move the discussion of the term "zeroth" to a subsection, and (4) rewrite the resulting article for a more encyclopedic style. See also a later section of this talk page. Marc van Leeuwen (talk) 08:06, 10 April 2010 (UTC)
Excuse me. I meant exactly what I said. If I meant Ordinal number (linguistics) I would have said so. Please read the article I linked Ordinal number - it explains the matematical concept. The linguistic concept is a derivative of the mathematical concept. Roger (talk) 07:39, 13 April 2010 (UTC)
So excuse me. Obviously you meant this article is about the order type of the empty set (the class of well-ordered sets with 0 elements). Or maybe about its unique representative the empty set, possibly viewed as a realization of the number 0. So perhaps you can explain why you think this article is about that notion. Or why one would need a separate article about that particular ordinal number, distinct from empty set and 0 (number) (none of the other finite ordinal numbers have any article as far as I know, and they appear to be no less interesting; they don't even have a collective article). Marc van Leeuwen (talk) 10:56, 13 April 2010 (UTC)

Zero based indexing[edit]

It's common to use zero as the starting point for measurements of continous quantities. This makes it easier to scale. This also holds for the discrete case, but isn't mentioned here. I'm not sure how to work it in though. —Preceding unsigned comment added by (talk) 06:07, 14 September 2007 (UTC)

Overall the article needs to be rewritten...[edit]

...however by someone who isn't up at 4 AM. All the comments are good, also the reference to should be dropped, it adds nothing.

This topic is worth keeping, however. —Preceding unsigned comment added by (talk) 10:17, 23 November 2007 (UTC)

More than three years later this article is still incredibly annoying. The spirit is: "We are all nerds, right? And nerds like zero-based numbering, yes? So everything nice we can think of concerning zero-based numbering can be accepted as facts fit for an encyclopedia". Still needs to be rewritten (or simply deleted). -- (talk) 13:47, 16 March 2011 (UTC)
The style of this article has much to be improved, and now that it's title is no longer "zeroth", there is lot's of stuff that simply doesn't belong here. But there is no connection between nerds and zero-based numbering suggested in this article, so I don't see your point. It is a fact that zero-based numbering is used (a lot), without being universally adopted (in contrast to for instance using digits starting at 0 in positional notation, which makes that a non-topic), so it seems quite a legitimate subject for an article. It should of course not concern advocacy for or against zero based numbering, but arguments that have been given can very well be cited. You just removed the only reference of this article relevant to this subject, which is not the way to start improving it (I restored it). I would be very interested to know about situations where using or not using zero-based numbering makes an objective difference (for instance do compilers on average produce equally fast code for algorithms coded using one-base or zero-based indexing, all other parameters being unchanged?). This kind of information may not be easy to obtain, but if possible this article would be a good place to find such information. If you can supply any relevant facts, or published opinions, please help improve this article. Marc van Leeuwen (talk) 14:27, 16 March 2011 (UTC)

Ground floor[edit]

In the article it says: "Some buildings in the British English speaking world refer to the ground floor as floor 0". This is also the case in other countries in Europe. Could somebody that knows more about this specify where in the world counting floors starts at zero? (talk) 16:19, 28 November 2007 (UTC)

In South Africa lift (elevator) buttons are usually labeled "G" for the ground floor. The first floor is the one above the ground floor. Basement levels (often used for parking) are usually labeled 1G, 2G, 3G... with the number increasing as one goes down. Some lifts do use "0" for the ground floor but I have never heard anyone actually say zero floor - always ground. Roger (talk) 16:37, 25 June 2008 (UTC)

The first is still the first[edit]

A comment above addresses the "other than computing" section. The "In computer programming" section has a similar problem.

The first item of a Pascal array declared var a : array [1..100] of integer has an index of 1. The first item of a Pascal array declared var b : array [-10..+10] of real has an index of -10. The first item of a Pascal array declared var c : array [] of 0..255 has an index of red. Who could disagree? Likewise, the first item of an array in C or Java, has an index of 0. Arrays don't need or have a zeroth item. That's not to say that no one in computing uses the word "zeroth" to mean the initial item of an array or list, but it is unnecessary and confusing when they do. It's even more confusing when they say "first" but mean "second", etc. Many computer scientists and programmers would never use this jargon. I would suggest that the use of "zeroth" in computing be flagged as "nonstandard".

The first chapter of a book might have a number of 0, or it might have no number at all, as is common in fiction. (Picking a novel off the self at random to verify this, I was surprised to find the chapter nearest the front was titled "1967". I don't think it was the 1,967th chapter.) If I don't put page numbers on the pages of an article, the first page is still the first page; if I renumber the pages so that the first page is labeled "1" or "i" or "0", it's still the first page.

The problem with the article is that it confuses labels with adjectives. The words "first," "second," etc are adjectives that indicate a position. The labels "0", "1", etc are labels. As an analogy, a dog might be named Blue or it might be coloured blue. It would be wrong to call a dog named Blue "the blue dog" unless the dog really was coloured blue. A lot of the article talks about sequences whose first item is labeled "0", this is interesting but not relevant to the topic.

I think the word "zeroth" has a few uses in math and computing. Here's one: It's well known that a quadradic is a second degree polynominal, so a constant is a zeroth degree polynomial -- although you could call it "a polynomial of degree zero". Similarly it might make sense to talk about a zeroth order approximation, when it is well understood what a first order approximation is -- although you could always say "an approximation of order zero". (talk) 12:17, 18 February 2008 (UTC)


How it the word pronounced? I have a problem figuring out how the transition from the "o" to "th" should sound. Roger (talk) 23:03, 15 July 2008 (UTC)

There are pronunciations hereand here that rhyme it with "both". But I usually pronounce it zero-eth. — Carl (CBM · talk) 01:24, 16 July 2008 (UTC)
The one that "comes naturally" to me (I speak South African English) also rhymes with "both" - but with a slight "w" sound inserted. A sound halfway between "both" and "growth". I wish I knew IPA! Roger (talk) 05:49, 16 July 2008 (UTC)
See also Talk:Ojibwe grammar#Zeroeth Person
—DIV (Melbourne, (talk) 06:18, 3 October 2008 (UTC))


Wouldn't 1/0 be one zeroth? (talk) 14:47, 12 January 2009 (UTC)

It would be reasonable, of course. But 1/0 only exists in some numeral systems (such as the Riemann sphere), and even there it's easier to just say "infinity" than "one zeroth", so I don't see much use of the word as a denominator. -- Jao (talk) 15:27, 12 January 2009 (UTC)


Should mention the use of "1th" for the next element after the 0th instead of "1st". In the case of a zero-based sequence, the zeroth element is the "first". "The one coming, occurring, or ranking before or above all others" —Preceding unsigned comment added by (talk) 05:42, 17 January 2009 (UTC)

What's your source? "Oneth" is in Wiktionary but without any sources. Many Jargon File mirrors (but not, it seems, the latest version of the Jargon File itself) says that "oneth" would be logical but is never used. -- Jao (talk) 11:34, 17 January 2009 (UTC)
Maybe logical, but not much help. "Zeroth", "oneth", "twoth", "threeth", but the fifth in the list still has to be "fourth" (the sixth can be "fiveth" though). There is no way out of the ambiguity created by using "zeroth", unless a whole new range of ordinal numbers is created, which is of course would make the whole notion zeroth pointless. Marc van Leeuwen (talk) 17:57, 10 April 2010 (UTC)

j mod N[edit]

I wrote

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.

This was "clerified" to

... modulo operator, which can make the index wrap-around properly.

I think this clerification loses the point. If the array's index is 1..N, the programmer needs to either adjust the result of j mod N by adding 1 each time or treat j mod N == 0 as a special case; if the index is 0..N-1, no adjustment is needed. Better wording is invited. —Tamfang (talk) 23:04, 26 May 2009 (UTC)

Comic books[edit]

Don't comic books usually start with an Issue 0? (talk) 21:56, 31 July 2009 (UTC)

I'm not aware of any examples. Zap Comix has a zero, but it appeared after #1. —Tamfang (talk) 02:04, 5 August 2009 (UTC)

Wrong-headed article[edit]

I find the form of this article very annoying. Most of it is about 0-based indexing (and 0-based redirects here), which is a widely used convention that a lot can be said about (and in favor of). But its title "zeroth" is a marginal neologism of dubious utility that has no strict connection with 0-based indexing (although one may suppose its popularity is dependent on that of 0-based indexing). In any case there is no necessity to use (or approve of) the term "zeroth" when using 0-based indexing. I've recently changed the lede to separate the issues clearly, focus on the issue that is the title, and give some reasons that one might object against the use of "zeroth" (more recent edits have left the lede in a somewhat sorry state though, like defining the zeroth element of a 0-based sequence as its first element, which has a sweet irony to it). Arguments against use of certain terminology are hard to source, since those who oppose will simply refrain from using it without motivating (but arguments have been given earlier on this talk page). But my real concern is that a separate article on 0-based indexing (currently a curious redirection) should exist with none of the "zeroth" stuff to it. So I propose that either such an article is split off, or otherwise that this article be renamed and the "zeroth" discussion be placed in a subordinate section. (For the record, I'm entirely convinced of the merits of 0-based indexing, and always use it in my (mathematical) publications even if it is likely to go against the readership's habits, but I never use "zeroth", or for that matter ordinal numbers at all (except "first" in the meaning of "initial"). Non 0-based indexing can be useful in rare cases like the sequence 1,12,13,14,... though.) Marc van Leeuwen (talk) 09:00, 14 March 2010 (UTC)

Needs better reasoning[edit]

Every integer is congruent modulo N to one of the numbers 0, 1, 2, ..., N − 1, where N ≥ 1. Because of this, many arithmetic concepts (such as hash tables) are more elegantly expressed in code when the array starts at zero.

This doesn't make any sense. In the same manner, we could say;

Every integer is congruent modulo N to one of the numbers 1, 2, ..., N − 1, N where N ≥ 1. Because of this, many arithmetic concepts (such as hash tables) are more elegantly expressed in code when the array starts at one.

It is only because the modulo operation as usually implemented (for non-negative inputs) has result in the set 0, ..., N - 1 that code is more elegant with array indices starting at 0. —Preceding unsigned comment added by (talk) 07:42, 18 January 2011 (UTC)

Is there any evidence that anyone has ever defined (including purely mathematically) modulo the second way? --Cybercobra (talk) 06:56, 19 January 2011 (UTC)
Modulo arithmetic is purely defined by stating that the differences of equivalent numbers are divisable by the chosen N. There is no need to define standard representations mathematically. Which numbers are chosen in practice to represent each class is arbitrary. Often 0 to N-1 are chosen, but for example the 12-hour clock uses 1 to N. −Woodstone (talk) 09:32, 19 January 2011 (UTC)
I've now added references to modulo operation to try and address this. --Cybercobra (talk) 03:27, 8 November 2011 (UTC)

Removed claim about usage of "zeroth" in computer science[edit]

Above it was often already mentioned: the use of "zeroth" instead of "first" to refer to the first item of an array is neither widespread nor correct. The first item is the first item, even if it is addressed as array[0]. It also wouldn't avoid confusion, but create it: if a[0] is the zeroth element, is a[1] the first? If so, one would assume there is no a[0]. If it is the second item, where did the first item go?

Anyone who wishes to undo this claim should back it up. -- (talk) 02:14, 8 November 2011 (UTC)

The text you removed is almost entirely explanatory. The few minor prevalence statements are easily rectified. --Cybercobra (talk) 03:20, 8 November 2011 (UTC)

Dubious unsourced supposition in Origin section[edit]

On July 4th, 2015, someone added a big paragraph at the start of the Origin section that doesn't have any citations, and that doesn't appear to make logical sense. It's just as easy with jump-if-zero (e.g. jcxz or jecxz in x86) to write backward order loops whose last loop index value is 1 as it is to write them with the last loop index value being 0, the former having the decrement just before the jump-if-zero, and the latter having the decrement after the jump-if-zero. The paragraph even mentions "decrement and jump if zero", in which case, the last iteration has index 1, not 0. The array indexing argument that was already there made much more sense, and has actual citations from relevant sources to back it up. I'd strongly recommend either providing some credible citations to justify the claim that assembly loops with jump-if-zero are "The primary origin of using zero in enumerating data entities in computer programming", or removing the whole paragraph. Ndickson (talk) 02:18, 8 July 2016 (UTC)

@Ndickson: I assume you talk about my edit "21:54, 4 July 2015‎ Purgy Purgatorio". In this edit I certainly did not want to express any impossibility, and also no special difficulty to implement index ranges starting with 1. Additionally, I also did not want to refer to any x86 architecture, but strictly had in mind the most early "von Neumann" architectures with one "accumulator" and one index register dedicated to address calculation, and evaluation of jump conditions based on accumulator content "all bits clear" (= 0), or "all bits set" (= -1), only.
I wrote a lot of machine code myself (to set up a symbolic assembler and loader/linker), taught serious coding in assembly language, and I was also sufficiently in contact with the development of HLLs on academic level to have been able to observe the increasing dissemination of indices starting at zero, triggered by the principles I tried to point to.
In any case, if you are convinced to improve this article by deleting this big paragraph, please, feel free to do so. I will not edit war or similar on this. Of course, I consider it also to be way beyond my interests to start a rescue mission for any word I wrote, nevertheless, in the light of the above, you might perhaps find improving content, or might be aware of some sources to point to. Purgy (talk) 11:02, 9 July 2016 (UTC)