Talk:0 (number)/Archive 1

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Older comments

The comment that modern languages use zero-indexing is somewhat misleading, because it isn't because of technical merits, but because of the popularity of C. It's no problem for the compiler to convert the one-indexing preferred by humans (or indeed most any indexing) to the zero-indexing used in the machine code. However, since C used zero-indexing and became so popular, most programmers are used to it. That's probably the reason it's used in most later languages.

"The year zero does not exist. Instead there is a "zero point" in time between the years [1 B.C.]? and 1."

What?

Yes, I think we should remove this rather obscure interpretation until someone can provided an authoritative justification for it. - MMGB

But it is correct that in our current system of timekeeping, the year following 1 B.C. was 1 C.E., isn't it? --AxelBoldt

Yes. The reasoning about a zero point is incorrect, though. The reason there is no zero year is that, as I'm sure Axel can confirm, zero hadn't been invented yet when this calendar system was made. The way I prefer to think of it is using the same logic as call 19XX "the twentieth century". We are simply in the 2001st year.--BlackGriffen

I'm not sure whether zero had been invented yet, since I don't know when people started to use the BC/CE method of labeling years. Anybody? --AxelBoldt

BCE CE didn't come in to use until the 20th century (might have been used earlier, but it seems to be an invention of political correctness). Let's see:

" The Gregorian calendar is the one commonly used today. It was proposed by Aloysius Lilius, a physician from Naples, and adopted by Pope Gregory XIII in accordance with instructions from the Council of Trent (1545-1563) to correct for errors in the older Julian Calendar. It was decreed by Pope Gregory XIII in a papal bill in February 1582." from http://www.geocities.com/CapeCanaveral/Lab/7671/gregory.htm

Not really authoratative, but it seems accurate enough. I thought that the calendar had been proposed earlier, in which case there would be no ambiguity. Had the Europeans learned of zero and the arabic number system by then?--BlackGriffen

No, thats the calendar. The system of chronology (the numbering of years) is separate from the calendar. Our current system of chronology dates back to Dionysius Exiguus (or however you spell him), c. 500 CE. Back then, awareness of the number zero was rather lacking, since people used Roman numerals, which lack a symbol for zero. By 1582 CE, by contrast, the number zero was well established (people increasingly used Hindu-Arabic numberals), but as I said, thats the calendar, not the system of chronology. -- SJK
This is not the case. There is no year 0 not because 0 hadn't been invented, but because years are ordinal numbers, not cardinal ones. The year 1 was the first year of the C.E. Year 2 was the second, 1999 was the 1,999th, etc. Year 2 BCE was the second-last year BCE, year 1 was the last, etc.
For support, we may turn to the French Revolutionary Calendar. Did they call their first year 0? Of course not; they called it 1. (Well, I.) And this was well after the invention of 0.
There's no year 0 for the same reason there's no 0th of January or 0th month. Anyway, Cecil Adams of the Straight Dope did a brilliant exposé on the whole mess more than ten years ago - it may be available at [1].- montréalais

The Zeroeth Symphony

I don't want to step on the toes of the learned Wikipedians working on WikiProject Numbers, but I want to bring to their attention a little tidbit on the number zero: while the ordinal zeroeth is rarely used, 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 about 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. Del arte 21:56, 16 Feb 2004 (UTC)

Very interesting. I've added this to zeroth. 4pq1injbok 03:52, 3 Aug 2004 (UTC)

Someone needs to clarify here or in null about the computer defintion of zero as not being "empty" or "void" like null is. In computer terms, if I am not mistaken 0+x=x while null+x=null. Right?

Zero in Mathematics

I don't like the comment that "x/0 is also the definition for infinity". This requires thinking of infinity as a number, which generally isn't done because it makes arithmetic messy (what is 0×∞? what is ∞+∞?) Having said that, ∞ is viewed as a number in the Extended complex plane. In any case it doesn't seem to make sense that this is the "definition" for infinity. There are different definitions for infinity in Mathematics used for different purposes, and each must be defined very carefully.

0 (number) or 0

How does 0 get to re-direct here?? For all other numbers, the numeral without the (number) suffix is for the year. 66.245.87.127 01:04, 4 Nov 2004 (UTC)

I suspect that the redirect was made by someone who thought that there was no year zero, which is true only in the modern Western calendar. Both astronomical years and Hindu years have a year zero. I propose that the current article '0 (year)' be renamed (moved) to '0' so that the unmodified number refers to the year as all other bare numbers do in accordance with the Manual of Style: "A page title that is just a number is always a year." It would still not be an entry in the Wikipedia timeline. Of course, the current redirects as well as the disambiguations at the top of both articles and zero (disambiguation) would be changed accordingly (they are either wrong or somewhat lacking at the moment). Joe Kress 19:03, Nov 4, 2004 (UTC)

Distinguishing zero from O

In paper writing one may not distinguish the 0 and O at all, or may add a slash across it in order to show the difference, although this sometimes causes ambiguity in regard to the symbol for the Null Set.

"Null Set" should either be Null set (no capital S for "set") or empty set. I think it should be empty set, considering the information on notation on that page, and the absence of any information on null set. Brianjd

Someone changed the article to say that letter O is more rectangular than digit 0. In the default font used by wikipedia this is not true on my screen. For me digit 0 has straights on four sides and rounded corners, while capital O is more oval shaped. How about your screens? −Woodstone 18:11, 2005 May 28 (UTC)
The only place I can recall seeing "more rectangular" letter Os is on license plates. It seems we have several ways that have been used to distinguish the characters, including "ovalness" (elliptical eccentricity?) "squareness" and slashing. I've also seen fonts where the zero has a dot in the middle. --Yath 23:30, 28 May 2005 (UTC)

Paragraph temporarily removed from History section

I have removed the following from the History section (it followed the sentence on Indian mathematicians year 300):

The earliest documented independent use of zero as a numeral is attributed to them. However, though this concept of the zero is documented as a contribution of ancient Indian thought, it is recognizably ludicrous for us to suppose that ancient Egyptian mathematics could have become as advanced as it was (see also Moscow and Rhind Mathematical Papyri and golden ratio [see Corinna Rossi, Architecture and Mathematics in Ancient Egypt, Cambridge University Press, 2004, pp. 23-56]) without such an idea of "nothingness."

The reason is that I'm unsure what is meant here. "Independent use" suggests (to me) use as a number (as in "zero brothers"), but immediately following that comes as a numeral, i.e. digit (as in "101 brothers", or more likely, "101 cousins"). The sentence preceding this deleted paragraph also seems to deal with the numral zero. The lines on Egyptian mathematics and Papyrus Rhind - a recent addition - seems to deal with the number.

Another thing that is unclear to me is what the golden section's got to do with it.

It would please me if someone could clarify these issues and reinsert the paragraph.--Niels Ø 02:12, Apr 3, 2005 (UTC)

First sentence in the paragraph stated: "The earliest known decimal digit zero is documented as having been introduced by Indian mathematicians about 300." "Independent use" was interpreted as referring to "use as a decimal place holder." Perhaps the paragraph was intially awkward to begin with. At any rate, referring to Timeline of mathematics and Egyptian mathematics, it is obsurd to believe that nearly 5000 years ago, ancient Egyptians were able to calculate π as 4×(8/9)² (or 3.160493...), with an error of slightly over 0.63 percent, and then suddenly hit an "intellectual wall" and totally stagnate intellectually for nearly 2 millennia afterward (before finally succumbing to the conquests of outside tribal warriors) without ever even contemplating this notion of "nothingness." Golden ratio is another such number including "0" as a decimal place holder. (But also is it certainly fascinating to note an ancient Egyptian knowledge -- many millennia ago -- of this number's existence!) Psychologically and mathematically, are we to really believe that in those 2 millennia no one single Egyptian mathematician ever thought about representing "nothingness" somehow? Speaking in the Science of Psychology now, History records only a few hundred years requisite for ancient Greek mathematicians to progress to some notion of "zero" concurrent with their ideological development of similar mathematical ideas. If it took the Greeks only a few hundred years, why would it take Egypt several millennia, facing the fact that the Greeks studied mathematics in Egypt? Please refer to the following quote:
"...there must have been much more to Egyptian mathematics. We know that Thales, Pythagoras and others visited Egypt to study. If there were only applied arithmetic methods as we have seen in the papyri, the trip would have had little value. But where are the records of achievement? Very likely, the mathematics extant was absorbed into the body of Greek mathematics -- in an age where new and better works completely displaced the old, and in this case the old works written in hieroglypics. Additionally, the Alexandrian library, one place where ancient Egyptian mathematical works may have been preserved, was destroyed by about 400 CE." [2]

Some historians believe that our ancient Roman ancestors destroyed more than just ancient Egyptian civilization and society, not to mention totally obliterating their peoples from the face of the Earth (but yes, was it the Romans? or Persians? or Greeks? or the Arabs in the end? or ...? We cannot point fingers here, because we have no definite knowledge). Some historians believe that our ancient ancestors plundered specialized knowledge of ancient Egypt and conspired to publicly declare those ideas (to us, their children) as their own. Note, for example, the Great Pyramid of Giza. Please read the article on that page. Why are we so confounded in this modern day for an explanation as to how it might have been feasibly constructed? Some are saying advanced engineering while others are claiming advanced alchemy!!! Note also the Suez Canal. Why would the ancient Egyptians dig such a monumental canal over 3000 years ago if they didn't possess a need to pass thru? -- 209.150.67.45

The principle error made by 209.150.67.45 is the assumption that the ancient Egyptians used decimal fractions — they did not. They always used proper fractions like 1/2, 2/3, 3/4, 1/4, 2/5, etc. and their sums. For example, 8/9 would have been represented as 1/2 + 1/3 + 1/18. See Ancient Egyptian Numbers (210KB). In the first example provided by 209.150.67.45, 4×(8/9)² (or 3.160493...) from Egyptian mathematics, the decimal fraction is the modern equivalent of 4×(8/9)², it was not used by the ancient Egyptians. The second example, Golden ratio, as its name implies, was a ratio or a proper fraction — the decimal fraction is only provided for our understanding.
However, I do not doubt that the ancient Egyptians understood 'nothingness', as I think all languages include such a concept. That is a principle problem with virtually all histories of numbers, and particularly the history of zero — they only discuss its symbolic representation, like 0, totally ignoring the word zero. Hence we have the totally false notion that the concept of zero was unknown in Western Europe before its symbol was introduced in the twelfth century. — Joe Kress 21:17, Apr 3, 2005 (UTC)
[Please] do not break up another user's comments. It belittles their words. You may reword your response accordingly. And please sign your posts. See Wikipedia:Talk page — Joe Kress 10:45, Apr 4, 2005 (UTC)

Sorry, the assumption is yours. You may not accurately state, for example, that the Egyptians never put dots of red ink on their noses just because we don't have any paintings showing this. There is insufficient evidence [and too few documents surviving] to back your statements.

For example, for all we know the ancient Egyptian priests may have hidden knowledge from their general population (and the rest of the world). [This is the common argument invoked today to explain ancient Egypt's monumental pyramid constructs and other achievements. No other theory works.] As a matter of fact, by the logic you seem to be using in your statements, you must conclude this to be true, because otherwise we would have documents today to expose our ignorance and eliminate all modern confusion surrounding the construction of the Great Pyramid of Giza and the Suez Canal. Nevertheless, this argument about "usage" is irrelevant, as the next several statements show.

[Referring to pi,] we know that the ancient Egyptians had knowledge of this number. Whether they used it or not, we may not accurately say. [However they certainly did use it in the design of the Great Pyramid of Giza!!] We do not know! There is insufficient documentation to accurately support your statements. However, as you can plainly see, pi is 3 + (fractional elements). Knowledge is power. If we know that they knew about these improper fractional elements, we cannot say they never used them. After all, we are talking about several millennia ago. None of us was around to verify.  :)

[Referring to the golden ratio,] same statement similar to above. And... it is absolutely amazing that they knew about it and used it in the design of their structures (as Rossi found they did in over 55 ancient structures analyzed)!!!

[Referring to Joe's final paragraph in the above arguments...] Agreement! Documentation shows that the symbol was introduced in the twelfth century. We cannot say that the ancient Egyptians did not have a similar or identical symbol just because we don't know about it from the few documents surviving. Please see Alphabet. There you will learn that History is being rewritten as we speak. If you open a 2004 Merriam-Webster Dictionary [3], for example, you will find a history of the Latin Alphabet very much different from what is posted in Wikipedia, because their history written in 2004 is limited to what is recorded in surviving documents, and it is now obviously blatantly incorrect!

In other words, in the above statements you are limiting yourself to what you see. You are not imagining possibilities. When one society conquers another, like criminals taking over a victim's home, what do you think might happen? We must use our imaginations to get a better picture.

But from the few remnants we have, they seem to have been far more advanced than has been commonly speculated. Unfortunately, they are no longer here to tell us. [--209.150.67.45]

/* Joe is correct about "belittling." I have revised the above statements for clarity. Some interesting arguments here! Thank you Joe and 209.150.67.45!! --Roylee

Perhaps you fella's might be interested in this fascinating reference, written by The Rev. Paul Barton, Ph.D. (Additional Reading: [4].):

"The earliest people in the Americas were people of the Negritic African race, who entered the Americas ... [for the 2nd time] about thirty thousand years ago in a worldwide maritime undertaking that included journeys from the then wet and lake filled Sahara towards the Indian Ocean and the Pacific, and from West Africa across the Atlantic Ocean.... Some of the ships used during the ancient times, perhaps earlier than 7000 B.C. (which is the date given for cave paintings of the drawings and paintings of boats in the now dried up Sahara desert) are similar to ships used in parts of Africa today. These ships were either made of papyrus or planks lashed with rope, or hollowed out tree trunks. These ancient vessels .. not only ... criss-cross[ed] the Atlantic but they traded out in the Pacific and settled there as well all the way to California.... It has been proven through linguistic studies, religious similarities, racial similarities between the Afro-Olmecs and West Africans, as well as the use of the same language and writing script, that the Afro-Olmecs came from the Mende-Speaking region of West Africa, which once included the Sahara. Sailing and shipbuilding in the Sahara is over twenty thousand years old. In fact, cave and wall paintings of ancient ships were displayed in National Geographic Magazine some years ago. Such ships which carried sails and masts, were among the vessels that swept across the water filled Sahara in prehistoric times.

.  .  .  .

In fact, there is evidence from ancient East Indian chronicles ... of the geat scientific advancement of the Black prehistoric inhabitants of the Indus Valley Civilization (6000 b.c. to 1700 b.c), who built flying machines, who had flushing toilets, cities on a gridlike pattern, and many of what we may call "modern" conviniences [sic]. About 20,000 years ago, the present-day dried up and desertified Sahara had an aquatic civilization where the Africans who lived on the edges of the giant inland sea, built large ocean-going ships. [5] -- Happy reading!! Roylee

To top all this off ... fella's ... ancient Egyptians had knowledge of decimal systems as early as 3100 BC!! See [6]. Do we really need two or three thousand years to pass by before fractional elements may enter into such a system??? Do you suppose ancient Egyptians knew about it ... but we have no record??? -- Roylee

Please remember, Wikipedia is not the place for idle speculation. References to a Reverend so-and-so's highly unusual theories is not valid substantiation for anything. At most, it may be presented somewhere in the Wikipedia as an intersting theory. But let's focus on established historical facts - and let's focus on the subject matter here - ZERO (the digit and the number) - please--Niels Ø 08:22, Apr 11, 2005 (UTC)!

Cleanin gup, merging

0 (number), 0 (disambiguation), and Zero (disambiguation) need to be cleaned up. I'm moving everything to the number, and not the spelled-out english title; and moving dab content to its own page away from the number/numeral article. +sj + 20:25, 12 May 2005 (UTC)

computers consider zero to be positive

It appears that computers consider zero to be positive. This is because the most common representation of numbers is the 2-complement, so a negative number always starts with the bit 1. Since zero starts with a bit 0 it is considered a posistive number.

No, this is not true. In two's complement, a "0" sign bit only indicates that the number is not negative. (With floating-point numbers (namely IEEE 754), there is both a positive and negative zero.) --P3d0 13:35, July 12, 2005 (UTC)
Some computers have both negative and positive zero. See one's complement. --A D Monroe III 20:31, 18 October 2005 (UTC)
Most CPUs have a special "all zero" attached, which makes the point of whether or not it is even moot. It's more important in computer science that it is a cruial asymmetry to the ABS()_function (other lesser repercussions are not as interesting. Early Java gave us a Math.abs() function, but since the range of say a byte is -128 to 127, the implementation has no good choice when presented with Math.abs( (byte)(-128) ). If one anticipates this issue, brava... but there are a half-dozen primitives to remember that this is an issue.

I have a serious grievance with the statement that zero "may or may not be" a natural number, particularly the smug assertion that if you think zero is not a natural number you are not a mathematician.

Repent for your tone when you couple it with falsifiable content.

I read the guidelines, but this ignorance must be eradicated like rats or pigeons; it's mathematical vermin.

Investigate the issue on Wolfram's site, and read 4 books written before the 70s on the topic.

Wolfram will set you straight.

The Matural Numbers are a non-terminating series that begin at 1 (ONE) amd whose next elementa is 1 greater than the previous. In the domain of natural numbers, division by zero is ungrammatical because THERE IS NO ZERO, THERE IS NOT EVEN NULL, only no remainder during division. It is NOY a valid Natural Number--that's why there's blanks and out-of-band .

The Romans did many great things, but they did nothing with the advances of the Greeks, consequently Merriam-Webster shows--from day one--a blank space in the Roman Numeral table. It's clear from the history that educated people of that time were limited to a single word, which to most meant Nothing/Void/Out Of Bane in a universal sense rather than a value that causes exceptional attention to the changes in the governing rules.

Then our Indian friends push through, give it a glyph--once that is accepted, mathematics is free from empiricism--and the rules governing the operators change due to DbZ. As one moves from one mathematical "calculs" to the next

Wolfram's approach to

Integers follow in the western world, but they're for bookish accountsl.0 Then we get integers, with negative numbers, but in software the problem/proficiency the register constrictions in and bytes and range/ , but I coden to

Similar complications arise S be t,Read a goddamn book. The history of mathmetatics is p This issue then infects all numeriimitive —Preceding unsigned comment added by KlangenFarben (talk • contribs) 07:21, 19 February 2008 (UTC)

Just curious...

...Is there any issue over whether or not zero is considered a number, at least, in the same way one and two would be? I was always wondering this. >.> -- A Link to the Past 09:02, July 16, 2005 (UTC)

In the past, zero was not considered a number - the article discusses the development of the concept at some length. However, it has been considered a true number for a long time, longer than negative or imaginary numbers. Zack 22:29, 16 July 2005 (UTC)

aught??

I'm sorry, but when and where was zero called "aught"? Surely, this should read "naught or nought", while "aught" is the precise opposite of zero, meaning "something"? 83.78.191.122 13:23, 16 October 2005 (UTC)

Another paragraph removed from the history section

I have removed this paragraph from the history section.

The zero was invented by inhabitants of India around the sixth century CE. The earliest zero on record, an inscription of Zero on Sankheda Copper Plate was found in Gujarat, India (585-586 CE). In Brahma-Phuta-Siddhanta of Brahmagupta (7th century CE), the zero is lucidly explained and was rendered into Arabic books around 770 CE. From these it was carried to Europe in the 8th century. However, the concept of zero is referred to as Shunya in the early Sanskrit texts of the 4th century BCE and clearly explained in Pingala’s Sutra of the 2nd century.

The part about Brahmagupta is redundant with existing discussion under "First use of the number", and the other part (the Sankheda copper plate, Pingala's Sutra, etc.) is unsourced. This text seems to have been lifted almost verbatim from a Hindu evangelical website which I do not find credible; all Google hits are either also copied from that site, or are Wikipedia mirrors. I'd be happy to see mention of the copper plate and Pingala's Sutra return to the article if accompanied by a credible source citation. It should also be corrected so as not to contradict the discussion of Mayan and Babylonian mathematics.

Zack 17:54, 3 November 2005 (UTC)

Zero in the Middle Ages

I've added to this section to make clear that zero was in common use from the thirteenth century for calculation. Also, mentioned the modern myth about the church banning zero as this comes up from time to time. --James Hannam 17:53, 15 December 2005 (UTC)

Is it even?

Is zero even? Why? I guess, the answer also should be included in the entry. --rydel 14:12, 18 December 2005 (UTC)

Yes it is, for the same reason that all other even numbers are even (0/2 = 0, an integer). Please do feel free to wedge that into the article somehow - right now I don't see a good place. Zack 19:53, 18 December 2005 (UTC)
I second that, could it please be put into the article somewhere as soon as somewhere reasonable is found. Cheers, darkliight 04:58, 9 January 2006 (UTC)

Sure zero is even. Any number taking on the form 2n is even, n = ...-2,-1,0,1,2,... for n=0 we have 2n=0. Thus zero is even.

Well... Zero is even at the mathematic point of view, not in the pratic... if you divide the zero in two parts you won't have a pair of "fractions of the nothing", but the zero...
Then, seeing the etimology of the word odd in portuguese (ímpar), it results in two terms:
Ím (ausence) + par (pair)...
Since you can't have a pair of nothings, zero can be considered odd in the pratic view of the mathematics (in the theory it is even...). (PS: I am a student of mathematics from Brazil) 200.153.221.40 01:30, 9 April 2007 (UTC)
On the contrary, you can divide the empty set into two equal parts, both of which are empty. To put it another way, an empty set is the disjoint union of two empty sets (which are all the same set, but that's aside from the point). Likewise, you can put an involution on the empty set without any fixed points (the empty function), and partition it into pairs (the empty partition), and relate its elements into pairs (the empty relation). These concrete realizations of the evenness of zero sometimes have practical applications.
I plan to write a new article on the evenness of zero, simple though the subject is. It may ultimately be merged here, or into Even number, or there might be a joint summary style structure. Melchoir 21:01, 27 August 2007 (UTC)

Stone in Saqqara pyramid?

In Fred Schuh's book, The Master Book of Mathematical Recreations, §§251-254, is mentioned a step-pyramid type puzzle involving multiples of 7.

§254 references a stone apparently found in Saqqara and created by Imhotep (Fig. 122); I am not sure if a scan of the stone would be allowable here, but the gist of it is that this stone has glyphs that appear to be numbers - decimal numbers even, including the 0 in its modern digital sense. It doesn't appear that these glyphs make any sort of sense except as being taken as numbers, either.

Has anyone else seen this stone? It's clear that it's significant in the history of the 0, but I have not been able to find any other references to Dr. Kirederf (despite him being supposedly "the well known Egyptologist" according to Mr Schuh), Eugaheht, the Saqqara stone or similar other than the book itself - I am not sure if this tale is true or apocryphal.

Amarande 23:24, 29 December 2005 (UTC)

1/0 = ?

shouldn't 1/0 equals infinity? Let me elaborate: 1/1 = 1; 1/0.5 = 2; 1/0.25= 4; 1/0.125=8; 1/0.0625= 16 ; ... ; 1/0=inf ?

  • In a way that makes sense, but we normally think of division as belonging to the field of real numbers, to which infinity doesn't belong. Check out appropriate pages at the Math Forum. Georgia guy 22:51, 5 January 2006 (UTC)
  • But 1/-1 = -1, 1/-0.5 = -2, etc, too. Then 1/0 must also by inference be -infinity, as well.

This attempt at inclusion opens a very large and destructive can of worms on traditional mathematics. Once we try to accept infinity as a number ... besides the fact that now we have a division with two results - which in itself contradicts the Fundamental Theorem of Algebra (a division is really the means of solving the trivial polynomial ax = b, with degree 1, and thus must have exactly one root per FToA with no exceptions), we have other unravelments -

For instance, in a similar vein then -

1/2 = 0.5, 1/4 = 0.25, 1/8 = 0.125, 1/16 = 0.0625 ; ... ; 1/inf = 0

But it's clear that any real divided by infinity is zero by this progression:

3/2 = 1.5, 3/4 = 0.75, 3/8 = 0.375 etc.

Or, more bluntly, we can write the series as 3(1/2), 3(1/4), 3(1/8) etc., and similar for other reals other than 1. In other words the basic point is what applies for dividing 1 by increasingly large denominators into infinity applies for all other reals as well. (OTOH I am not entirely sure of the interactions between infinity and complex numbers ...)

So now we've established that (any)/inf = 0.

But remember that dividing solves ax = b, which means that if b/a = x, then necessarily ax = b, also.

Which means that 0 * infinity = n, for all real n.

I'm pretty sure though that there's also a theorem guaranteeing that the product of any two constants is also a constant ...

Oops.

No, I don't think attempting to accept infinity as a number and thus defining x/0 is going to sit well in the mathematical stomach.

Amarande 04:02, 8 January 2006 (UTC)

  • Mathematicians are, however, happy to consider the matter geometrically. If we

consider the real numbers to be a line, then adding an extra point 1/0, the point at infinity, is one way of constructing the real projective line. Topologically it gives us the one point compactification of the real numbers. Gene Ward Smith 08:53, 5 March 2006 (UTC)

Bhaskara II had a similar view. See Division by zero. deeptrivia (talk) 04:45, 8 January 2006 (UTC)
You might want to tell this to the folks over at the Infinity page, because under the mathematics section, there's a big equation that says X/infinity = 0... The Disco King 04:39, 22 February 2006 (UTC)
In a paragraph preceding that equation, you can read this:
Infinity is not a real number but may be considered part of the extended real number line, in which arithmetic operations involving infinity may be performed. In this system, infinity has the following arithmetic properties:
If you want to write anything like 1/0=infinity, it must be preceded by a similar phrase to explain the context. More precisely, it would need to be the one-point compactification discussed in the Infinity article. But really, I do not think this article should get into that kind of complications.--Niels Ø 09:49, 22 February 2006 (UTC)

Logical definition

I've included Russell's famous definition of zero to supplement the current explanation ("For example, if the number of one's brothers is zero, then that person has no brothers. If the difference between the number of pieces in two piles is zero, it means the two piles have an equal number of pieces.") Not only does the logical definition introduce rigour but the original definition is circular. Mikkerpikker 15:03, 8 January 2006 (UTC)

Nonstandard analysis

I've removed the following sentence, which is at best highly misleading, from the article:

In any hyperreal field, zero is smaller in absolute value than any positive number, and so is trivially an infinitesimal. However, normally by an infinitesimal, we explicitly mean to exclude zero. For instance if dx and dy are infinitestimals, we can take the ratio dx/dy only if dy is not zero. Gene Ward Smith 01:13, 2 March 2006 (UTC)

Irrelevant additions

Does anyone agree with me that the following additions are infinitely extendable and have no relevance to the article?

  • In trigonometry, sin 0 = 0, tan 0 = 0, arcsin 0 = 0, and arctan 0 = 0.
  • Zero is one of three possible return values of the Möbius function. Passed an integer x2 or x2y, the Möbius function returns zero.
  • Zero is the first Perrin number.

−Woodstone 22:29, 20 July 2006 (UTC)

The first and third seem silly, so I'll delete them. The Möbius function bit isn't so bad, since it has a bit of content, but if someone deletes it too, I'll still sleep at night. Melchoir 03:45, 21 July 2006 (UTC)
Do you know the Perrin sequence? 3, 0, 2, 3, 2, 5, 5, 7, 10, 12, 17, 22, 29, 39... Anton Mravcek 16:21, 21 July 2006 (UTC)
So what? There are an infinity of sequences (and functions) that have a zero somewhere. The fact that 0 is in the sequence may say something about the sequence, but does not tell us anything about zero. The line does not belong in this article. −Woodstone 17:18, 21 July 2006 (UTC)
Exactly. The OEIS suggests about 80000 known candidates. Melchoir 18:51, 21 July 2006 (UTC)

Dell and zero

Ok, a bit off topic, remove this if it is in the way. Just wanted to mention that the zero fell off my keyboard and when I phoned Dell to have it fixed, the guy who answered did not know what a zero was, I used the article 0 (number) to explain. I don't think English was his first language. Once he realized what I meant said Ohhh, that is what a zero is, I know that number. HighInBC 23:14, 12 September 2006 (UTC)

Pingala, etc.

These references need a bit more research (and don't seem relevant if they are similar to Morse code, a ternary system)? The Pingala article also seems quite clear that this has little to do with zero, so perhaps we should clean this up? mfc 15:53, 20 September 2006 (UTC)

I'm not sure what you mean by "clean this up". Even if this means deleting it, I have no basic objection except to note that it will probably be added again by an Indian proponent. I have another objection to the following sentence, that he used sunya, void, to mean zero. That is not noteworthy because as far as I know, all languages have a word for nothing, and it is obvious to me that when applied to anything that is normally counted, like sheep or goats, can be translated as zero. In my opinion, the concept of zero has always been known, only a special symbol for it was a late arrival. — Joe Kress 22:05, 20 September 2006 (UTC)
The way I undertood it was that Sunya-which translated to void-was the name given for that symbol in Indian math, where its role as a placeholder was first developed. But that's just what I think.

--Sakredfire 07:42, 6 June 2007 (UTC)

The Law and Zero

Perhaps a section on Law and the number zero should be included. Example: Our apartment building was to have a bylaw stating that there can be no rental suites but the lawyers said that zero is not a number and so we had to make it "1" instead of "0". There may be other cases like this. Comments?

topher67

Grammar of zero

Perhaps this could be expanded upon, is zero singular or plural, e.g., there are zero comments but not *there is zero comment. Why is that? CoolGuy 03:47, 10 November 2006 (UTC)

In grammar many languages differentiate between one and "not one" - usually referred to as "plural". Zero is usually not considered identical to one and so "plural" is used when referring to zero. So, there are zero students in the class until one student came in. Be aware that indo-european languages originally had three forms, "singular", "dual" and "plural". This is where words like "both" comes from, we say "all three" but we say "both" rather than "all two". Again, the "plural" doesn't necessarily mean "plural" but rather "neither singular or dual" or "anything other than the aforementioned forms". As such it is a "bag case" or "miscallaneous" case that cover "anything that doesn't fit into the other" cases. Modern english and other indo-european languages have generally dropped the dual and only keep "singular" and "plural" where "plural" means "not one" rather than actual "plural", i.e. it also covers zero.

Of course, in ancient times they did not consider zero to be a number in its own right and so they would probably not use plural to cover zero. They would never say "there are zero students in the class", rather they would say "there are no students in the class". How this was reflected in the grammar they used at ancient times I don't know, however, you can then argue that "plural" in the latter form makes sense because there are neither 1 nor 2 students in the class, there are none and so a plural form comes natural as an "without reference to a specific count" as the "no students" do not refer to a specific count in the mind of the ancients as they did not consider zero to be a number or count.

salte 14:01, 15 December 2006 (UTC)

wikipedial medieval zero

See Talk:Number

Proposal: split off 0 (numeral) or 0 (digit)

This article is getting a bit long (36 KB), and it deals with both the number zero (the abstract concept of nothing, which is so useful in math) and the numeral/digit 0 (a little symbol that looks like an ellipse and should not be confused with O, although it's often pronounced "oh"). The two topics are mixed in together in a confusing way. It seems that there is enough material on the latter (typography, etc.) to split it off into its own article. Comments? Joshua Davis 00:15, 16 December 2006 (UTC)

Distinguishing zero from nothing

I would propose to leave out the confusing "As a number zero means nothing — an absence of other values". Alhough 'adding the number zero' has the same effect as 'adding nothing', in principle we have to distinguish between the concept 'number zero' and the concept 'nothing'. That distinction is no meaningless distinction, because 'adding nothing' is, contrary to 'adding the number zero', the refraining from any action. It implies that the number zero is not identical with ‘nothing’ ('nothing' is only nothing, and so it cannot be a number at all). Although ‘zero apples’ boils down to ‘nothing’, the number zero does not. The so-called medieval zero is no real zero at all (see the discussion about wikipedic medieval zero (Talk:Number 28). Jan Z 15:17, 2 January 2007 (UTC)


Zeroes or Zeros?

I notice some inconsistency in the spelling of the plural form of 'Zero'. What is the correct spelling?

Both spellings are correct, but you are expected to choose one of both. Here it's mixed as you noted. I have not found the exact difference (like -se or -ze for verbs like realise, .. : people assume it's a UK/US difference, while it's a within-UK difference historically). --82.35.101.136 11:47, 16 April 2007 (UTC)Marvin D. Martian

The zeros/zeroes discrepancy keeps me up at night, as Wikipedia articles (and any other document, for that matter) should have standardized spelling. Both the American Heritage Dictionary (US) and the Cambridge University Dictionary (UK) ambiguously list the plural of zero as "zeros" or "zeroes," so it is not a UK/US difference (as far as I can tell). Unfortunately, I can find no other evidence, historically or didactically, that should indicate what spelling is proper. I was born, raised, and learned grammar in Tennessee, and have always spelled it zeroes. I am interested to see what other users have traditionally used. At some point, I think it would be prudent to choose one over the other. Derekpblank 00:53, 4 August 2007 (UTC)

The Concise Oxford Dictionary only gives 'zeros' as the plural of the noun. The -es form is used for the verb (as in "it zeroes in on the target"). Webster gives 'zeros' as the plural (with 'also zeroes'). Charles Seifre, in his book Zero – The Biography of a Dangerous Idea, uses 'zeros'. On the other hand, Robert Kaplan (The Nothing That Is – A Natural History of Zero) uses 'zeroes'. Other writers avoid the problem by only using 'zero' in the singular Google reports 'zeros' about three times as common as 'zeroes'.

Net: it seems rather arbitrary, and perhaps regional. It looks as though 'zeros' is the most common -- and it has the advantages of parsimony and avoiding any confusion with the verb form. mfc 11:17, 4 August 2007 (UTC)


History of Zero

I think the two history sections need to be combined. Also, there is some disagreement about whether Long Count examples were found outside the Maya homeland. Whether yes or no, we need a cite to back up whichever version of the story is presented. Cbdorsett 06:36, 14 February 2007 (UTC)

The entries under History do not discuss zero used alone, as those under History of zero do, hence they must remain distinct in some manner, although I don't know what would be the appropriate sub-heading for the first sub-section. — Joe Kress 07:51, 15 February 2007 (UTC)

digits and zero in various languages.

I removed the translations, as they don't belong in here, maybe they should be in wiktionary.

A few additional examples follow.

  • Arabic: Sifr
  • Catalan: xifra, cypher, amount; desxifrar, to decode; zero, zero
  • Czech/Slovak: cifra, digit; šifra, cypher
  • Danish: ciffer, digit
  • Dutch: cijfer, digit
  • French: zéro, zero
  • German: Ziffer, digit, figure, numeral, cypher
  • Italian: cifra, digit, numeral, cypher; zero, zero
  • Malay: sifar
  • Norwegian: siffer, digit, numeral, cypher; null, zero
  • Persian: Sefr
  • Polish: cyfra, digit; szyfrować, to encrypt; zero, zero
  • Portuguese: cifra, figure, numeral, cypher, code; zero, zero
  • Russian: цифра (tsifra), digit, numeral; шифр (shifr) cypher, code
  • Slovenian: cifra, digit
  • Spanish: cifra, figure, numeral, cypher, code; cero, zero
  • Swedish: siffra, numeral, sum, digit; chiffer, cypher
  • Serbian: shifra, cypher, figure, numeral
  • Turkish: Sıfır
  • Urdu: Sifer, Zero

bogdan 13:40, 23 February 2007 (UTC)

How many digits does 0 have?

I cannot find a source that tells how many digits 0 has. I suppose people assume it has one because it is represented by one digit (0), but I have a few arguments that say it doesn't have one digit
  • There are 9000 numbers with four digits, 900 with three, 90 with two, and ... 10 with 1
  • The first number with four digtits over the first number with three is ten, three digits/two digits=10, two digits/one digits= ... infinity (or undefined)
  • The logarithim of the first number with four digits is 3,three 2, two 1,one ... -infinity
Does anyone have a definite answer, or an idea for an argument, on how many digits 0 has?

Indeed123 21:21, 10 March 2007 (UTC)

It's often a special case in digit-counting, but the most consistent value is zero. In n digits, you can encode 10n values, from 0 through 10n-1 The number of digits in x is the least integer n such that x ≤ 10n-1, or x ≤ 10n. For x=0, this works out to n=1.

This matches the extreme case of "delete leading zeros", and is often used in bignum implementations.

71.41.210.146 16:34, 30 April 2007 (UTC)

In other fields?

The in other fields article is rather trivial. Should we consider removing it?--Cronholm144 22:41, 19 May 2007 (UTC)

Quotations section should be moved to WikiQuote

I'm not sure how to do it. Also, it is causing formatting issues.--0rrAvenger 15:41, 26 May 2007 (UTC)

Rules of Brahmagupta

The rules of Brahmagupta are very important, but I think they are in the wrong place. His ideas about zero should certainly stay, but the others I'm just going to move to the page on the book. If anyone disagrees, please move it back. Indeed123 15:01, 2 June 2007 (UTC)

Rectification

on the article about zero, the para saying that hindus invented the zeroes by thhemselves has been removed. It is true that the mayans have used it..but the hindus took no greek or chinese etc. "help" in creating it..It would not be an exaggeration to say that all middleage(i.e., when the muslims came), European mathematics was exclusively obtained from India carried and edited or refined forward by the arabs. Evidence of High indian maths is not available as the moslem conquerers destroyed most hindu texts, libraries after stealing the knowledge, plunging a superior nation into the dark ages.Even arab scholars like al-beruni were against the destructive attitudes of the conquerers, and for inctance, severely censured mahmud of ghazni for destroying such an advanced culture... Also, plenty of chinese maths was influenced by buddhist missionaries who went there and hindu prisoners of war

Hieroglyphics?

I have removed the sentence "It means "courageous one" in hieroglyphics." from the article pending some sort of contextual explanation. Speciate 20:26, 25 July 2007 (UTC)

No divisors?

I thought all intergers divided zero (actually, I'm pretty sure they do). Why does it say "N/A" in "divisors"? Shouldn't it say "all numbers"? —Preceding unsigned comment added by 200.199.119.74 (talk) 04:52, August 27, 2007 (UTC)

Comparing this table with that appearing on other number pages shows that divisors lists numbers that will divide the article's number (here 0) evenly, without leaving a remainder. In other words, it lists the results of factorization. One requirement of factorization is that the given number is the product of the factors, which must also be divisors. This would exclude 0 itself because it cannot divide itself. A better term to use in the table would be factors. — Joe Kress 20:40, 27 August 2007 (UTC)
I disagree. The infobox already has a field named "factorization" where the reader should expect to find the results of factorization. In the next field, named "divisors", the reader should expect to find the divisors of 0, full stop. Placing N/A in this field suggests that 0 does not have any divisors or that the concept of an integer dividing 0 is ill-defined, both of which statements are false.
There is a legitimate question as to whether the statement a|b should be defined when a = 0, and in fact, my abstract algebra text declines to define it in this case. Even if one does define it, it makes a difference whether the definition is "b/a is an integer" or "na=b has a solution". In the case of 0|0, the former statement is either false or again ill-defined, while the latter statement is true. So one could, as a matter of convention, write either "all integers" or "all nonzero integers". Either one could be cited with a quick trip to Google books.
To save us the headache, I'll just write "all numbers", which should be sufficiently vague to avoid controversy. Melchoir 02:22, 1 October 2007 (UTC)

history of zero

history is not chronological, it would be more understandable if it was. —Preceding unsigned comment added by 68.212.234.91 (talk) 23:16, 14 November 2007 (UTC)

request to remove "both"

I request that we consider removing "both" from the first sentence in the lead paragraph. What do you think? --Kushalt 22:16, 6 December 2007 (UTC)

I think we should attempt to reach uniformity for the first sentences of the 10 articles 0 (number) through 9 (number).
There is a kind of category confusion; properly speaking, we ought to distinguish between "0 (number)", "0 (digit)" "0 (glyph)" and "zero (name)". There is a number, usually represented by "3", but the same number can be represented by "11" in the binary system, or the Roman numeral "III", and also by "003" or "3.0" in the decimal system. However, a simple "3" is the "normalized" decimal representation. Because of the way the decimal system works, and because 0 ≤ 3 < 10, we use a single digit to represent that number. That digit is not a number, but a (one-character) symbol used for representing numbers. (Aside. This is similar to the distinction between the word "I" – the first-person singular pronoun, as opposed to the second-person "you" and the plural "we" – and the capital letter "I", lodged in alphabetical order between "H" and "J" and having "i" for its lower case. If certain reformers of the English spelling had had their way, we might be writing "Ie" for the pronoun.) To put that symbol for the digit on paper, or on a computer screen, we use a single character for the symbol "3"; that character has a shape, called a glyph. To talk about the number, we use a name, which is "three". We use the same name for the digit and the character/glyph. In other languages, the name is different: drei, trois, etcetera, even if the number is the same. In some other cultures, the glyph is also different: ٣, or ৩, or ௩ (see Hindu-Arabic numeral system), even though the mapping from number to sequence-of-digits is the same. Strictly speaking, in different typefaces the glyph is different: 3 versus 3.
Therefore, I'd prefer to seee something along the lines of:
3 (three) is a number, the natural number following 2 and preceding 4. In the decimal system it is represented by a single digit "3". The word "three" is used as the name of both the number and the digit.
This is easily generalized to all single-digit numbers, with only 0 having no natural predecessor; instead we can state that it is the smallest natural number.
I see no reason to say that 0 is a glyph. Our article Q simply states that Q is a letter; it does not say that Q is a glyph. It does not even mention the term "glyph". If the article discusses glyphs (some have a section on the evolution), we can simply use the first time "the glyph for the digit D", where D is the appropriate symbol, and use "the glyph" in the remainder.
 --Lambiam 02:38, 7 December 2007 (UTC)

Verification needed

In the History of zero section, I added the following paragraph based on Sangi o koeta otoko by Wáng Qīngxiáng and The Nine Chapters on the Mathematical Art:

In China, counting rods were used for calculation since the 4th century BCE and Chinese mathematicians understood negative numbers and zero, though they had no symbol for the latter. The Nine Chapters on the Mathematical Art, which was mainly composed in the 1st century CE, stated "(when subtraction) subtract same signed numbers, add different signed numbers, subtract a positive number from no-entry (zero) to make a negative number, and subtract a negative number from no-entry to make a positive number."

After that, Arthur Rubin added "veryfy source" tags. Could someone please remove the tags? I shouldn't do it myself, although I'm sure about the meaning of the paragraph above. The original line is as follows:

正負術曰: 同名相除，異名相益，正無入負之，負無入正之。 (wikisource)

Here 無入 literally means no entry and actually means zero. - TAKASUGI Shinji (talk) 00:43, 19 December 2007 (UTC)

I don't think we can use wikisource as a "source", unless it's a reprint with a reference to the original source. In any cases, do the sources actually assert that the zero was used c. the 4th century BCE (or, to be precise, on a date which maps to that date using modern date references)? — Arthur Rubin | (talk) 01:06, 19 December 2007 (UTC)
Do you doubt Wikisource? If so, I can provide several sources on the web:
The Nine Chapters on the Mathematical Art is a well-known book in ancient China. You can also find books on it. We can only say with the current sources that zero was used in China in the 1st century CE. I can hardly imagine they didn't use zero while using negative numbers, but I don't have a source for zero in China in the 4th century BCE. Anyway, someone who can read Chinese or Japanese other than me should edit the article. - TAKASUGI Shinji (talk) 02:36, 19 December 2007 (UTC)
Of course I doubt Wikisource. Doesn't everyone? Wikisource and Wikitionary can be used as related subjects, but not as sources. I think it might be best if someone other than yourself should remove the tags, as you point out, but I think they may very well be accurate. — Arthur Rubin | (talk) 02:41, 19 December 2007 (UTC)
Just for clarification, I cited the original text of The Nine Chapters on the Mathematical Art from Wikisource, not the claim that ancient Chinese used zero. The rule itself proves the use of zero, though. - TAKASUGI Shinji (talk) 00:36, 20 December 2007 (UTC)
I don't read Chinese. I assume that the occurrence of "(zero)" in the translation is an editorial insert, meant to clarify the preceding "no entry". Can we be sure that this is not a novel interpretation? Is it absolutely clear in the context that "no entry" stands for a number? The meaning of the whole passage is rather obscure; I hope this was not a textbook meant for self-study.  --Lambiam 09:52, 19 December 2007 (UTC)
Actually, zero is the standard translation by mathematical historians. The no-entry is my editorial replacement to clarify the original word 無入, which is not used today. The modern Mandarin word for zero is 零 (líng), which originally meant a small remainder, not zero. This change suggests mathematicians understood zero but laypeople didn't. Quite similarly, in English, you can say oh, naught, nil, etc. instead of zero. - TAKASUGI Shinji (talk) 00:36, 20 December 2007 (UTC)
P.S. You write: "based on Sangi o koeta otoko by Wáng Qīngxiáng". In what sense is this based on that source? Is it a paraphrasing of information from that source, and can it be considered a reliable source? The title is Japanese but the author's name is Chinese; is this a translation of a Chinese original?  --Lambiam 10:01, 19 December 2007 (UTC)
It's a reliable book. Here's a link to Amazon Japan: [7] It's written in Japanese by a Chinese mathematical historian, who became a Japanese national in 2000. He got a Ph.D. in science at the University of Tokyo and is a professor at the University of Yokkaichi now. Is that enough? I used the book to show the translation of the rules of zero of The Nine Chapters on the Mathematical Art. Classical Chinese is so different from Mandarin it's not good to cite only the original text. - TAKASUGI Shinji (talk) 01:03, 20 December 2007 (UTC)
So, do I understand the following correctly:
  1. The information "Chinese mathematicians understood negative numbers and zero" is not your interpretation of the text from The Nine Chapters, but paraphrases the interpretation given by Wáng Qīngxiáng.
  2. The quoted passage from The Nine Chapters is a translation into English of a Japanese translation of the Classical Chinese original, where the Japanese translation can be found in "Sangi" o koeta otoko.
  3. However, you have replaced "zero" (零?) in the Japanese translation by "no entry (zero)" to make the translation more literal.
If that is the case, I think you should write just "zero" (and not "no entry"), and use only "Sangi" o koeta otoko as a reference. Even better is if you can cite a published English-language translation, such as:
Shen Kangshen, John N. Crossley, Anthony W. -C. Lun (editors). The Nine Chapters on the Mathematical Art: Companion and Commentary. Oxford University Press, USA (1999). ISBN 978-0198539360.
I don't have access to a library, so I can't check that source myself.  --Lambiam 19:08, 20 December 2007 (UTC)
Correct. I can understand the original text, though. I believe it's good to have a link to and a citation from The Nine Chapters on the Mathematical Art on Wikisource, because it's easily accessed by everyone. - TAKASUGI Shinji (talk) 00:53, 21 December 2007 (UTC)
I've made an edit to the article that, hopefully, everyone finds satisfactory.  --Lambiam 13:25, 21 December 2007 (UTC)
Thank you very much. - TAKASUGI Shinji (talk) 22:50, 21 December 2007 (UTC)

In computer science : the index size convenience point

I think there's something lacking in the "In computer science" section in the advantages of 0 indexing. One of them is indexing. Let's say you're on a very simple 8-bit architecture, and that you're trying to allocate/have access to an array containing 256 elements.

With 0 indexing, you can use indexes from 0x00 to 0xFF (255) to access all your array elements. But with 1 indexing, you would have to use indexes from 0x01 to 0x100 (256)! That takes an index with more than the necessary 8 bits. That's quite a problem, as these type of situations happen quite frequently, depending on the kind of programming you do. --62.147.133.191 (talk) 19:03, 19 December 2007 (UTC)

You are undoubtedly right. Do you happen to know a reliable source that mentions this issue, so that we can include this in a verifiable way in the article?  --Lambiam 21:18, 19 December 2007 (UTC)
No. But we can do it like we always do, add that to the article, and have a "citation needed" thing. Someone will eventually bother with finding a citation. --62.147.133.191 (talk) 07:35, 20 December 2007 (UTC)
You don't need an extra byte to store an index for a 256-element array, regardless of the first index. If it starts at 1, just store the index - 1. - TAKASUGI Shinji (talk) 09:52, 20 December 2007 (UTC)

Indian Contribution

I think the history section needs to be started off with wordings which sound something like this. "The origin and history of zero can be traced back to the Hindu/Indian civilization." The article in its current form supports this statement. Why always a western bias in the scientific history and origin of everythingSrinivasanram1 (talk) 17:34, 26 December 2007 (UTC)

The Hindu/Indian zero was the first decimal zero. All instances before that were for non-decimal zeros—sexagesimal, vigesimal, Roman numeral, etc. — Joe Kress (talk) 08:12, 28 December 2007 (UTC)
The Indian zero was the first decimal non-blank zero. Chinese have been strictly decimal from the beginning and they wrote arithmetic rules on zero and negative numbers in the 1st century CE, but their zero was a blank. - TAKASUGI Shinji (talk) 14:47, 28 December 2007 (UTC)
"Eurocentric" was the word I was looking for.Srinivasanram1 (talk) 04:59, 29 December 2007 (UTC)

If anything this article needs to be more "Mexicentric". While, yes, the earliest long count calendar to specifically have a zero dates from 36 BC, the earliest examples of the long count calendar itself, which requires the 0 to work, goes back many centuries before that, before the Indian or any other version of 0. --86.148.57.131 (talk) 17:12, 8 January 2008 (UTC)

Actually, the earliest Long Count of any kind is that of 36 BCE (7.16.3.2.13), which did not use a zero. Indeed, none of the earliest Long Counts (36 BCE–162 CE) use zero according to Mesoamerican Long Count calendar#Origin of the Long Count calendar. When written in bar-dot form without glyphs the Long Count requires a zero to work. However, a Long Count written with glyphs that name the units (baktuns, katuns, etc.) does not need a zero, even though they were usually written with a glyph that meant zero when a the Long Count contained a zero. Thus the article must be reworded so that it does not support the misconception that the earliest Long Counts used a zero unit. Nevertheless, the earliest Long Counts that did use zero are still quite early. — Joe Kress (talk) 08:38, 10 January 2008 (UTC)

Spanish version

The Spanish version of this aricle seems to have a different history of zero. Why the difference? Rmhermen (talk) 22:54, 12 January 2008 (UTC)

The Spanish version is really weird. According to its Google machine translation, zero originated in the "Belgian Congo, under the Empire Mweangh" possibly as early as 15 AD, but with an earliest certain agreed upon use in 327 AD. But according to early Congolese history, the earliest empire was the Kingdom of the Congo (1400-1914) whose leaders had the title Mwenekongo. This appears to be the source of the garbled Spanish phrase. Furthermore, Congolese oral tradition was not set to writing until the late 16th century. The translation then states that that zero came to Europe through Marroquis, which is Marrakesh, Morocco. This is reasonable for the Arabic version arriving in Europe via the Moors. It says the word zero comes from Swahili fejr (sifuri) via Arabic sikd (ṣifr) via Russian (tzifra) (usual English transliterations in parentheses). Thus the word arrived by a very circuitous route quite different from the concept. But the Swahili word actually came from Arabic, not vice versa. The Russian probably did come from Arabic (via Greek), but was not the source of any Western European form. Somehow the Almajesto (Almagest} was written in 204 AD by Titus Vespucio, instead of about 140 AD by Ptolemy. A possibility for Titus Vespucio is Vespasian, Roman emperor from 69 to 79, whose full name was Titus Flavius Vespasianus. I have no idea what to make of "In 343 AD Zsnewinya creates a number system that was not zero and it was a simple positional system." I can't identify Zsnewinya, and 343 is nowhere near any important date in mathematics of which I am aware. Within the same paragraph two sentences later, Indians are mentioned for the first and only time! — Joe Kress (talk) 06:34, 13 January 2008 (UTC)
Don't take it seriously. It's surely a vandalism by 190.51.158.88 [8]. It'll be reverted. - TAKASUGI Shinji (talk) 09:12, 13 January 2008 (UTC)
I was more than a bit suspicious of the Belgian Congo bit. I reverted it - it is just a shame that the vandalism there got edited for links and grammar several times with no one noticing the content change. Of course, I have seen it happen in English as well. Now if I could only remember why I was trying to read the article in Spanish?? Rmhermen (talk) 17:52, 13 January 2008 (UTC)