Talk:Numeral system

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Contents 1 Older discussion 2 Nenets source 3 Number system- Not Numeral 4 Split the page 5 Deleted material 6 Chinese, Japanese, Korean should be grouped under same system in the numeral template 7 History - where are the refs? 8 Degrees into minutes??? 9 Sumerian notation? 10 Requested move 10.1 Survey 10.2 Discussion 11 External Links 12 Base 8 in Proto-Indo-Europeans 13 Back to numbers 14 Important or not? 15 Examples on how to do basic arithmetics? 16 The five and twenty system 17 unique representation

[edit] Older discussion

Archive 1

[edit] Nenets source

No source cited on the Nenets base 9, and can't find any other info. -LinguisticsStud

The burden is on the uploader. No cite, no write. Here's the text I deleted:

"The Nenets language once used a base-9 system (nonary), but has since shifted to decimal under the influence of Russian. The word yúq originally meant 9, but took the value 10 on account of Russian influence; so in current Nenets the word for 9 is xasu-yúq, lit. 'Nenets yúq', whereas 10 is simply yúq, but in Eastern dialects also lúca-yúq, lit. 'Russian yúq'."

Whoever uploaded it is welcome to reupload it with a cite. See Wiki guidelines on the policy. Cbdorsett 09:57, 29 January 2007 (UTC)

[edit] Number system- Not Numeral

Knuth does a nice history of "Number Systems" in the Art of Computer Programming.

Text after text describe radix based and/or positional "number systems".

Here are a few I've glanced at recently.

- “Number Systems and the Foundations of Analysis”; Elliott Mendelson; Academic Press, Inc; 1973

- "Encyclopedia of Computer Science"; Ralston, Reilly, Hemmendinger; Nature Publishing Group; 2000

- "The Art of Computer Programming - Semi Numerical Algorithms"; Knuth; Addison Wesley; 1981 (Oh. Look. The Wikipedia article on "numeral systems" cited this one, including the term "number systems" in the citation.)

If Wikipedia has a basis in credible literature for renaming "Number Systems" to "Numeral Systems", it should be prominently displayed in the article.

Plain and simple, a number system provides meaning for a numeral. Without the number system, the numeral is just a string of characters. The number system maps the numeral to the number which it represents. The actual type of the number system is (numeral -> number). Calling it a "numeral system" is no more descriptive then calling it a number system. That doesn't matter any more; Not even a little. The convention is established and Wikipedia doesn't get to change it. It's a "number system".

Someone needs to rewrite this article, eliminating the term "numeral system".

And by the way, in the page on "number systems", reals, integers, complex, imaginaries etc are sets not systems.

I don't think Wikipedia is changing a standard convention; it's just adhering to one. So you cite some examples that are exceptions. The words "number" and "numeral" have standard meanings; Wikipedia is following them.

You are wrong to say the reals, integers, etc. are simply sets; they are sets with structures; some (reals, complexes) are fields; some (integers, quaternions) are rings but not fields; in the case of the reals, the ordering, rather than just the algebraic operations, is often taken to be part of the structure. The reals are just one number system, but there are many different numeral systems by which one can identify particular reals. Michael Hardy 23:24, 6 November 2005 (UTC)

... and I am suspicious of the claim about Mendelson's book. Can the anonymous poster describe its topic with enough specificity to make it clear that it's about numeral systems and not things like the reals, rationals, etc.? Michael Hardy 23:27, 6 November 2005 (UTC)

... and now I see: right at the top of the article, very conspicuously, it says: "Occasionally the term "number system" is used for this concept, but...". I think that is full and sufficient answer to this anonymous poster's concern. Michael Hardy 23:48, 6 November 2005 (UTC)

[edit] Split the page

This page describes to different things and this causes problems on pages that link to it, like Arabic numerals. This article should be split into:

• An article about systems employed to represent numbers, probably Numeral system, i.e. here.
• An article about sets of glyphs used to this, probably Numerals, which redirects here.

What say you? Zocky 22:46, 7 December 2005 (UTC)

Not necessary yet. I don't see sufficient content on glyphs that can be extracted from a description of how they are used. Davilla 22:05, 8 February 2006 (UTC)

[edit] Deleted material

• In French, the word neuf still means both 9 and 'new'.

This was parenthetical so I'm assuming the contributor wasn't sure of him/herself. I've tried to look up the history of neuf with no luck. Is there a French equivalent to the OED? Unless both senses can be traced back centuries, I think it's better to leave it out.

• [Base-12 systems were popular] because the year has twelve months.

BS. The twelve months are a more recent invention than the number system.

• The bases that were used in the past or used today are 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 16, 20, 60.

First of all, it would be much more interesting to note the number systems used naturally, before discussing the computing age. Second, this "summary" adds some other bases that aren't discussed in the article. Davilla 22:14, 8 February 2006 (UTC)

"Neuf" (new) comes from Latin novus and "Neuf" (recent) from Latin novem. They come from similar-sounding (but different) Indo-European roots. AnonMoos 22:38, 8 February 2006 (UTC)

[edit] Chinese, Japanese, Korean should be grouped under same system in the numeral template

Chinese, Japanese and Korean numerals are all based on Chinese numerals AND on the Chinese numeral system. The base ordering is also entirely Chinese (ordered by myriads 10^4 instead of thousands 10^3), the official written form of all three languages are also in Chinese characters (一, 二, 三, 四, 五, 六, 七, 八, 九, 十). It is ridiculous to separate the three if Hindu-Arabic are grouped under one; the differences between Chinese, Japanese and Korean numerals are merely linguistic (much like the difference between French and English counting of Arabic numerals). Japanese and Korean numerals are not genuine numeral differences and should not be classified separately in the Numeral Template on the right of each numeral-related page; instead they should be grouped together under a "Sinitic" category. Naus 03:23, 26 March 2006 (UTC)

Similarly, I object slightly to appending “Japanese” with Chinese in the table. I had changed it from Kanji because that is a Japanese word that literally means “Chinese characters.” The Japanese and Koreans are well aware that the characters are entirely of Chinese origin. MJ (t • c) 15:39, 15 November 2007 (UTC)

[edit] History - where are the refs?

I think there's some bold statements in the history section. I think the stuff about modular arithmetic is pretty weak.

"In China, armies and provisions were counted using modular tallies of prime numbers. Unique numbers of troops and measures of rice appear as unique combinations of these tallies. A great convenience of modular arithmetic is that it is easy to multiply, though quite difficult to add. This makes use of modular arithmetic for provisions especially attractive. Conventional tallies are quite difficult to multiply and divide. In modern times modular arithmetic is sometimes used in Digital signal processing."

I think this is supposed to be a reference to the Chinese remainder theorem or some interpretation therein. I see the following issues:

1. I'm pretty sure the specific examples about rice and armies was a theoretical idea used by another historian (need to find ref) to explain why the CRT might have been developed by Sun Zi. Sun Zi just quotes the problem with numbers, and I don't think makes reference to armies or provisions.

2. I think the statement that addition is harder in modular arithmetic is at worst wrong and at best confusing.

"The binary system (base 2), propagated in the 17th century by Gottfried Leibniz who had heard about it from China, came in common use in the 20th century because of computer applications."

I'm aware of Leibniz and binary numbers, but I had not heard the connection to China. I would assume the connection is somehow to the I Ching. Does anyone have a reference for this?

Thanks,--M a s 19:47, 5 May 2006 (UTC)

[edit] Degrees into minutes???

"and in our system of angular measure (a degree is divided into 60 minutes and a minute is divided into 60 seconds)"

Maybe I'm wrong here but that makes absolutely no sense. Since when has minutes been a measure of angle?

I don't know since when, but several hundred years, I'd guess. Many electronic calculators (especially slightly older models) can do conversion between angles in degrees with decimals, and angles in degrees, minutes, and seconds with decimals. E.g., 17.375° = 17°22'30", and 73.220644° = 73°13'14.32".--Niels Ø 14:02, 6 May 2006 (UTC)

The minutes and seconds here are not the same minutes and seconds used in time.

[edit] Sumerian notation?

Why no separate page for Sumerian numeral notation, given its foundational importance? I'd do it myself, but my books covering it are 2000 miles away and I have a hard time trusting webby sources... Anyone? JDG 05:28, 11 May 2006 (UTC)

I moved some of the History section to a new page titled "History of writing numbers" where I added 4 paragraphs on the historical origin of numbers in prehistoric Sumer. If you know where I can find gif files for archaic numerals and cuneiform numerials, please tell me and I will add them to History of writing numbers. Bob Best, 1:20am, 19 June 2006.

[edit] Requested move

[edit] External Links

There are two external links named [1] and [2]. I guess they are/were used as a reference - but of what? Should they be removed? Pedalist

[edit] Base 8 in Proto-Indo-Europeans

The evidence given for the use of base 8 amongst proto-indo-europeans doesn't make sense. A base 8 system only requires 8 digits, 0-7, therefore both 8 and 9 would be new digits for proto-indo-europeans. Application of Okham's razor would result in the conclusion they used base 9 based on this evidence and reasoning. If someone has access to the reference given for this snippet, could they look it up and check this? Make sure it is base 8, and check to see if any other evidence is given for base 8 (and why 9 is "new" but 8 isn't). Ooooooooo 00:29, 1 December 2006 (UTC)

Nenets --

Really need a source on the Nenets base 9 thing. Can't find it anywhere else.

I question the assertion "Zero to seven are the only possible digits." I believe most early numbering systems started with 1, thus the original digits in a base 8 system would be 1-8. This would also mesh with the "9 = new" postulate. None of this is in my area of expertise, but this statement immediately struck me wrong. I've changed it for now, but would be interested in hearing other viewpoints or if there are any relevant citations.

--EMU CPA (talk) 18:54, 29 May 2008 (UTC)

[edit] Back to numbers

I feel the article should be moved to numeral, since the topic is clearly the numerals themselves. That there is more than one numeral system is rather self-evident and could be explained more intuitively than making a disambiguation where one isn't actually required.

Peter ^Isotalo 20:45, 6 February 2007 (UTC) jesus loves you man

[edit] Important or not?

At the end of the article (in 'Properties of numerical systems with integer bases') a theorem is stated and proved. However the reader is not informed whether or not this theorem has any relevance or importance whatsoever. If some authors here think that this theorem can be interesting to some readers, then some kind of motivation for this should be stated in the article. Bob.v.R 11:11, 22 June 2007 (UTC)

No respons until now. Bob.v.R (talk) 18:33, 11 January 2008 (UTC)

[edit] Examples on how to do basic arithmetics?

I have contributed to the similar page in Swedish and I have some examples on how to do arithmetics in other bases (in this case, base 14). Maybe this is something worh including on this page aswell?

Position value	143	142	141	140
Memory		14
Number 1		0	12	5
Number 2	1	9	1	4
Difference	1	5	11	1

Paxinum 19:46, 13 July 2007 (UTC)

[edit] The five and twenty system

is (or at least was) used in Welsh counting. Numbers 1 to 10 are used, and then counted as 1-and-10, 2-and-10, 3-and-10, 4-and-10, 15, 1-and-15... The next major numbers are 20, 40, 60, 80 and 100 (no specific words for 30, 50, 70 or 90).

[edit] unique representation

The article contains the sentence:

...the usual decimal representation of whole numbers gives every whole number a unique representation as a finite sequence of digits...

What about 0.999...=1. Don't we have 2 different representations for the same number 1 here.--Shahab (talk) 10:22, 22 November 2007 (UTC)

But 0.9999.... is not a finite representation, 1.0 is. Every whole number can be represented in (at least, at most?) 2 ways, one with infinitely many 9999.. and one with 0. Paxinum (talk) 11:50, 27 November 2007 (UTC)