Talk:Positional notation

267: 246: 1190:. Astronomical numbers usually had a whole decimal number followed by six decimal fractional positions identifed with superscript Roman numerals. The fractional positions were called minutes, seconds, thirds, fourths, fifths and sixths (in Latin). The first two superscript Roman numerals have now degraded to simple marks, ′ and ″. If hours or degrees were the whole number, its fractional sexagesimal positions were still called minutes, seconds, thirds, fourths, etc. By the 19th century, thirds, fourths, etc. were replaced by decimal fractions of the seconds sexagesimal position. 1579:

the entire section about what digits and numerals are in the context of positional notation. Your version did not contain as much about 'numeral' as what I think it could have, and what you said about 'digit' was fine, just not as strongly related to 'numeral' as I hope I have now done, thoroughly. As far as using quotes or not and choosing between spelling-out or not, I think numerals and digits need quotes to turn them into "signs" to distinguish them from numbers, which are, in this simple case, pure, familiar, decimal magnitudes. I had to move the entire section further

2081:), but writing a definition that makes sense to someone who does not already understand the concept is harder. I remember I had trouble when I first came across this kind of thing 40+ years ago -- like: If numbers are used in the definition, isn't it circular? Is there such a thing as a number, separate from it's representation? (Yes, of course, but I had to get used to that idea.) If we use subscript to indicate base for a digit string, how is that base encoded? (Basically, if it was coded the same way as the digit string, it should always read "10"!) Etc. 471: 1039:. I tried to add an old version of this long time ago and some admins got all freaky on me and said that it wasn't allowed b/c you had to pay for something... But I'm trying again. Anyway I made it alot faster than my old one b/c its all client side and only requires javascript. Other than that it had all the same features as before. If somebody hosts it on their site and puts a link in the article to their site, I would like it if you would say on the page that you got it from my website. -- 461: 440: 213: 2301:(of base ten). More generally, a positional system is a numeral system in which the value of each digit has to be multiplied by some factor depending on its position for getting its contribution to the value of a number. In early notations, such as the Roman system, a digit has only one value: I means one, X means ten and C a hundred (however, the value may be negated if placed before another digit). In modern positional systems, such as the 2102:, with more details on the role played by the position. However, there is another issue in the article that requires clarification, the ambiguity in the meaning of the title: "Positional notation" may refer to any numeral system for which the value of glyphs may depend on their position. In this sense, Roman numerals is a positional system (VI ≠ IV). Or "Positional notation" refers to modern numeral systems in base 814:

repeated -- I retract the earlier complain about the second paragraph being confused, but I still find it confusing. The problem is that it says additive systems are better for arithmetic, but this doesn't seem right at all. Could this be explained? How does positional notation require memorization of tables? Does this mean multiplication tables? Perhaps this matter should be moved out of the article lead.

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been used in the whole number portion, so even they were not new symbols. Even more absurd would be to argue that medieval sexagesimal notation used 60 symbols — that system used decimal numerals that were used for the whole number portions of those numbers. An example is 365 dies 14 33 9 59 ... (365.242546219... days) used in the 14th century for the length of the tropical year in the

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delay after the pulse marking the beginning of data. If there were no pulses in a given time slot, that represented a zero. One pulse represented a one, five pulses a five, nine a nine. All computation was done basically by counting pulses; counting up past nine created a carry pulse. Subtraction was by counting down. Nikevich 01:29, 17 January 2012 (UTC)

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only used three symbols (ten, one and zero), while the Greek (Hellenistic) system used fifteen (nine letters for units, five letters for tens, and a symbol for zero). The symbols were additive within each position. Not even modern sexagesimal systems use 60 symbols, such as those used for time and angles—they only use ten (0–9) within each position. —

1659: 1683: 1335:, not a "set of symbols" (as that passage could be interpreted). Also concerning "a distinction needs to be made between a number and the that number", this seems to me not worth mentioning, because I take it to refer to the ordinary need to distinguish between an abstraction (a math number), and a symbol (a math numeral). 2079: 1368:

From my childhood when I first came across notations other than decimal, I recall a period of confusion untill I had gotten used to the distinction between a number as an abstract entity and its familiar decimal representation - a distinction that is emphatically NOT made when we first learn numbers.

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Time and angles are not positional notations. Time is broken up into some blocks of 60 (but also some of 24, 7, 356.24, ...). In the same way that English weights and measures are not positional systems, even though they are broken up into blocks of 12s, 3s, 4s, 2s, etc. Babylonian numbers do have 60

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The concept of infinity and the invention of transfinite numbers are not related to the representation of numbers as points on a line, but is a purely set theoretic idea. Irrational numbers were found as solutions of geometric problems that had no corresponding numeral (rational) representation, long

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We should remove the "Issues" section from this page or we should put it under "Applications" within a subsection called "Application Issues: Legal and Economics". I believe this problem should be addressed in context and not part of the overall description of the notational system. Also, if we want

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It might be of modest interest that the Friden EC-130 and EC-132 electronic desktop calculators (among the earliest such) used unary "notation" in their internal storage, which was serial, and recirculated stored numbers in a delay line. Each digit had its designated time slot, located by a specific

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A key argument against the positional system was its susceptibility to easy fraud by simply putting a number at the beginning or end of a quantity, thereby changing (e.g.) 100 into 5100, or 100 into 1000. Modern cheques require a natural language spelling of an amount, as well as the decimal amount

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I've implemented your first suggestion. Mathematically there is no need, but using the parenthesis does enforce what is happening to a student. In the second case though I can't see where the ambiguity arises, unless you are suggesting not using the universal convention that the digits 0-9 retain

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Also for mentioning different radixes/bases such as where “In base-16 (hexadecimal), there are 16 hexadecimal digits (0–9 and A–F) and the number” is mentioned, it can confused some users because using symbols 0-9 looks like decimal, when they could be hex numbers. I think it would be better to use

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A timid copyedit compressed my point to an "unseeable", two-sentence paragraph last month. This month, with your prompting, Vandium, I familiarized myself better with the article, edited more boldly, and emmulated some of the good math writers I've been reading by making my point clearly, and made

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Does it want to say "In order to present numerals in another number bases, a new distinction needs to made for the symbolic notation of the digit in any one position"? But this is just saying "The numerals of other number bases have different meanings than the numerals of base-10 number bases."

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The Babylonian numeral system, base-60, was the first positional system developed, and its influence is present today in the way time and angles are counted in tallies related to 60, like 60 minutes in an hour, 360 degrees in a circle. The Hindu–Arabic numeral system, base-10, is the most commonly

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Please do not over-complicate the lead. The lead should answer the question in a simple summary, formal definitions belong down in the body. In this article the section "Mathematics" gives quite an involved description, whether it is a formal definition correct I leave to others, but this is the

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I recovered the Babylonian and Greek non-positional forms because both are valid positional systems even though neither is positional within each position. They show that positional systems do not need a large number of symbols equal to their base, as you once stated. The Babylonian base-60 system

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is the article after I rewrote the section which here is called "Mathematics". First of all, this section is not about mathematics, just some random notes about positional notation that babbles on in different directions and doesn't do a very good job of explaining (in my opinion). If you disagree

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section. I had forgotten all about this mess, but my viewpoint is the same as yours: there is nothing positional about the unary system. (The reason that true base-1 positional notation doesn't have an article is of course that it would be completely useless, not being capable of denoting a single

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aside: romans did not commonly use the preceding lower order symbol for substraction. I reckon it would have been more like this: (plus signs aren't needed now that order means nothing) IIII XII = XIIIIII = X IIIII I = X V I = XVI combine, re order, re group sometimes the process would have to be

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I made the appropriate copyedits to the first two paragraphs. Also, BTW, I thought it not important to say "real numbers" can be represented in any number base. Firstly, integers can to. Secondly it is not on topic. Thirdly, I suspect any finite number can be represented by any base, and this

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that were normally used for all numbers. Unlike Babylonian numbers, Ptolemy only used sexagesimal notation for the fractional portions of his numbers. Those Greek numerals were simply Greek letters with assigned numerical values (e.g., α=1, ε=5, ι=10, τ=300), where numerals above fifty would have

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I'm sure that nobody wants you to pay to post the website. However, it is generally inappropriate to link to your own website. I looked at the link and your site is rather confusing, you seem to use base not as the numerical base, but as the list of digits. I'm not sure that this site is actually

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What the subject says. It can do fractions (most of the time) to a many places, you can make up a base with whatever characters you want as long as each digit is only a single character, it has a list of common bases to choose from when converting. Plus its GNU GPL. I think mine has more features

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I don't see how unary isn't a positional system. You could view it as a base 1 system (seems kind of obvious). Its drawback is that it can only represent positive integers. Standard rules for constructing any base_n number work for base 1. 1^0 + 1^1 + 1^2 + 1^3... The position is meaningless, but

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Possibly, but this would need a footnote for explaining "earliest". Also a search on the sources is needed for clarifying which numeral systems have been qualified as "positional" in the literature: Should the Babylonian system system be qualified as "positional" or simply as a "precursor of the

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It is well known that the easiness of cheque fraud has been made as difficult as it was before by marking the specified digits on their left and right sides by surrounding lines, so that an addition is easily detectable. So if somebody fears the fraud of his digits he adds these surroundings.

1397:. When I say "not worth mentioning" again here, my concern is mainly about stressing the meaning of "digit" to do it. Let's discuss the meaning of "digit". When that is clear, then the entry can be written however you choose. In any case, I'm sure we can agree that the distinction is made 1180:

This article is entitled "positional notation", so all aspects of that subject are appropriate, especially its history. I categorically reject your idea that Babylonian sexagesimal positions had 60 symbols. That is your "modern sexagesimal notation" voice talking. By that reasoning, Ptolemy's

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symbols, they just happen to follow a pattern which can be defined by only 3 symbols and placements. But that is really aside from the point, my understanding of this article is that it covers modern positional notation. To me that means the extension of the way we write decimal to any base.

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Also, there is really an important job to do consisting in clearly reorganizing all about base-p, decimal, p-adic, notation vs numbering vs numeral system: so many things are said about the same thing more or less correctly and more or less contradictionally in so many different places.

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When converting to decimal from hex or octal I use a multiplicative method. I was taught it at school in the '60s, I can't say I've seen it written down, but it seems much simpler than either the division or Horner's method. The method is simple to code even in shell scripts or AWK.

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I'm happy with that. I always worry when academic experts get too rigorous in a lead, I tend to assume the lead readers may be 14yo boys or non-technical older folk and phrase accordingly. The body is the place for rigour. I think you've got the balance pretty well here.

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I said Babylonian and Greek sexagesimal numbers were not positional within each position, because both were additive within each position. Thus a Babylonian sexagesimal position like <<<|| meant 10+10+10+1+1=32. The corresponding Greek sexagesimal position

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their meaning in all systems in which they are present. Subscripts work here where the text is processed, but are useless when computer sources are seen. Consider: 1234567 = 4553207 = 12d687. The last form is unambiguous, the first two can be confused.

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used system in the world today for most calculations. The binary numeral system, base-2, is straightforwardly implemented in digital electronic circuitry and used by almost all computer systems and electronics for calculations and representations.

1468:), but then I kept going so maybe I got carried away :). I’d like to know if there are any specific problems with my version; the revert message didn’t explain much. From memory these are some of the problems I had with the earlier version: 1092:

I have not been able to get this link to work any time that I have checked it, even when modifying the link to be ".com" instead of ".com.". If it's not corrected, it should be removed, as it is completely useless if it cannot be accessed.

2224:. This is wrong as I means one or minus one, depending on the position (XI ≠ IX), and similarly for X and C. I do not know how fixing this by keeping the lead short and clear, but we must not introduce assertions that are blatantly wrong. 1808: 1321:

In order to discuss bases other than the decimal system (base ten), a distinction needs to be made between a number and the digit representing that number. Each digit may be represented by a unique symbol or by a limited set of symbols.

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This isn't the actual computation someone would perform, but rather an attempt to replicate the abstract process the user of Roman numerals might engage in to perform an addition. For basic monetary transactions, it is slightly faster.

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HA I added it anyways. Now admins, don't be noobish and say you have to pay for it. I'm still confused about all that. In fact, I'm a huge fan of freedom (libre), and with simple web stuff like this free (gratis) generally comes with.

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There's a simpler notation for balanced ternary. Because the only non-zero magnitude is 1, it's simpler, typographically, to simply use + and - , i.e., just the signs, for the non-zero digits. Nikevich 01:19, 17 January 2012 (UTC)

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It's not easy to put a definition into writing that actually is helpful - that is, it's easy enough to write a definition that is correct and makes sense to anyone who already "gets it"; it's really just one formula (like

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A section titled "Exponentiation" where the images display how the digits are laid out, is there a way I can have consistent font so I can edit the image to display parenthesis like this (or simply have them in text):

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Without such memorization the student was not considered competent. Positional notation also requires memorization of multiplication tables. Only when a machine is used (like the abacus) are such tables not needed. —

1618:"It was likely motivated by counting with the ten fingers. " Lol. Maybe, but you'd need to chop off a finger or count one of them as zero. Is there much research into the history of the base ten number system? 2389:

1 1 x2 2 1 3 x2 6 1 7 x2 14 1 15 x2 30 1 31 x2 62 0 62 x2 124 0 124 x2 248 1 249

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I have serious doubts about that statement too. Roman numerals required the memorization of doubling tables (and possibly other multiplication tables) by everyone taking mathematics in school during the first

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I added "place-value notation", a term commonly used in U.S. schools, as a synonym for this type of notation. Based on the description I believe this is accurate, but please someone double-check me. Thanks.

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an important one, and I think it is far more easily grasped if you have a mental concept of number tied to positional notation. Can this be said in the article in a way that is not misleading?--

1750:(5100). Given that the characters "伍仟" can be inserted at the beginning to change the value, how does writing out the number on a check in Chinese prevent fraud (in this instance, at least)? 1520:. But these two concepts are distinct because a particular numerical value has different representations in different bases.”? But perhaps this point should be made further up in the article. 1516:

If the first paragraph and start of the second paragraph is meant to introduce Nø’s distinction of decimal numbers, how about saying something like “A decimal number represents a particular

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itself, to prevent such fraud. For the same reason the Chinese also use natural language numerals, for example 100 is written as 壹佰, which can never be forged into 壹仟(1000) or 伍仟壹佰(5100).

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It is exactly what you are doing: You start with the most significant digit (= coefficient) multiply by the base (= variable) and add the next (less significant) digit (= coefficient). –

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meant 30+2=32. But the corresponding medieval sexagesmal position was positional because it was the ordinary decimal number 32. Elsewhere, medieval numbers still used Roman numerals. —

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I added links to the corresponding mathematical ideas. Sadly there is little details provided about the construction. Both articles deal only with the decimal system.

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with my rewrite please let me know what about it bothers you. I'd be happy to make this more of a collaborative work, but I think it needs some major help. Cheers, —

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But that evades the rubric "digit". So how about "In order to present numerals in another number bases, a new set of digits is used that is not the set 0-9." —

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the article to make my points since, sectionally speaking, Numerals use the Base's concepts, and Digits use Notation's concepts and Exponentiation's concepts. —

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Explicitly mentioning (and even repeating) this distinction in an article on postitional notation in a general encyclopedia seems highly relevant to me.--

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The article linked in the upper right box convers bijective numeration only. There does not appear to be a entry for base-1 positional notation.

706:. Perhaps the reference to the new article in the present article should be in the introduction, as some sort of disambiguation, rather than in the 422: 412: 2962: 1793: 1225: 892: 679: 283: 2430:

is written for specialist theoreticians, not for mere system programmers like me. I scanned it but couldn't see anything on radix conversion.

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In 111, the three identical symbols represent one hundred, ten, and one, respectively, due to their different positions in the digit string.

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In practice it's usually simpler to trivially convert binary to octal or hexadecimal before performing the conversion if doing it by hand.

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modern positional system"? WP must reflect the common use, not the opinion of its editors. A reliable reference for these questions seems

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Positional notation greatly simplified arithmetic, leading to the rapid spread of the notation across the world. By adding a marker (the

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I'd say that's a good question - that is, I guess there is not one clear definition anywhere in the article. We might include

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In 555, the three identical symbols represent five hundreds, five tens, and five units, respectively, due to their different

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The use of quotes, italics and spelling for digits, digit values and other numbers seems arbitrary and potentially confusing.

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were all concepts that could only be discovered once the idea of a continuous number line was implied by positional notation.

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Would you consider the addition of "earliest" as above? The original form seems to have used IIII for IV and VIIII for IX.

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clear by describing the different number bases of a particular number, even without entering the statement I question. —

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The system works just as well for smaller bases: 0b11111001 (binary) to 249 (decimal), just a bit more long-winded:

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Confusion of letters and numbers proved a little too well for me: “Except one in some fonts? Which one? Oh, except

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to talk about 'fraud', we should provide better sources and explain why 'check fraud' is problematic in society.

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I think it's odd that the issue of fractional numbers is addressed in the section on base-60 but not in base-10.

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Roman system, a digit has only one value: I means one, X means ten and C a hundred. In a positional system the

2134:) is a method of representing or numbers based upon the position of the digit. In early notations, such as the 1501:, its numerals are commonly assumed.” compared with “. . . we learned with its numerals—are commonly assumed?!”. 1365:

In Babylonian base-60 notation, a digit is composed of several graphemes - if I've gotten the terminology right.

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In 111, the three identical symbols represent one hundred, ten, and one, respectively, due to their different

1543:. The distinction between a numeral and its various numbers is made most clear when doing base conversion. — 2779: 1629: 1757: 1162:

To be honest I don't know what you mean by positional within each position. Can you explain that? Cheers, —

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The real value of positional notation turned out to be its ability to invite the further study of numbers.

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that helpful in it's current form. It would at least help to have some explanation on that page. Cheers, —

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For simple addition and subtraction, the Roman numeral system is basically abacus-like; so for instance

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I, too, found that paragraph somewhat misleading. On the other hand, the notion of the real number line

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place to put it. I would suggest slightly rejigging the lead to simplify the explanation as follows:

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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needs commas or brackets before I can make sense of it: “The decimal system is widespread, and,

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suspicion extends into transfinites. I made it say "any number" instead of "any real number". —

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If you mean Positional digits alternating in sign, then there is now given: E.g. Knuth. –

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section. Apart from that, I suggest further discussion of these issues takes place at

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1 means one but 10 means ten and 100 a hundred. The "1" symbol has moved position.

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can sometimes mean an entire number written with of multiple digits (as used in

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I did some major rewriting of the article, which apparently wasn't appreciated.

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Category talk:Positional numeral systems#List of positional systems by base

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before positional systems came into use (or at least independent thereof).

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1 means one but 10 means ten and 100 a hundred. The "1" symbol has moved

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1 means one but 10 means ten and 100 a hundred. The "1" symbol has moved

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the fact—also stated—that it's obviously not a positional system) and

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of the digit means that its value must be multiplied by some value:

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should be boiled down to a minimum, with a link to the main article

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I completely agree about removing this section of kind of «issues».

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A citation needs to be given to a reliable source proposing this.

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In fact, except for the history section, this article is about the

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or a more leisurely one, like the one I've included in the lead of

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that the other links in this article. The link to my converter is

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Using the cited example: converting A10BHex to decimal (41227):

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I carried this paragraph in the article "Complex Base Systems"--

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But how can such a multi-grapheme, Babylonian, ""digit take-up

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Thereafter in the cited section, Horner's method is explained.

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Positional notation#Non-standard positional numeral systems

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Positional factors alternating in sign: Original research?

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Start with first digit: A x 16 =: -->

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It was likely motivated by counting with the ten fingers.

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sexagesimal notation used 60 symbols even though he used

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edit I initially wanted to fix the {{ndash}} usage (see

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I have addressed certain issues by creating the article

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positional notation? Making the distinction between a

1114: 2532:{\displaystyle A=\{a_{n}a_{n-1}\dots a_{1}a_{0}\}_{b}} 173: 2782: 2762: 2738: 2625: 2585: 2545: 2460: 2160:) the notation can be extended to include fractions. 1811: 895:(which confusingly says that unary is such a system 488:, a collaborative effort to improve the coverage of 278:, a collaborative effort to improve the coverage of 2826: 2768: 2744: 2724: 2611: 2571: 2531: 2263:, which has many pages devoted to numeral systems. 2073: 1391:and a number is explicitly stated in the article 642:13:56, 8 Apr 2005 (UTC)== Fractional numbers == 46:for general discussion of the article's subject. 2968:Knowledge level-4 vital articles in Mathematics 1734: 1648:2506 = (2 * b) + (5 * b) + (0 * b) + (6 * b) 932:it's a generalization of positional systems. 809:How is additive system easier for arithmetic? 187: 8: 2797: 2783: 2520: 2467: 712:talk:Non-standard positional numeral systems 2270:, that is the extension of any base of the 1216:Non-standard positional numeral systems (2) 2426:Quite possibly. Like most maths articles 1771:Is ″Positional notation″ defined anywhere? 1742:In the example of Chinese usage provided, 1724:Issues: Susceptibility to fraud in Chinese 539: 434: 329: 240: 2800: 2790: 2781: 2761: 2737: 2716: 2700: 2675: 2659: 2646: 2636: 2624: 2592: 2584: 2552: 2544: 2523: 2513: 2503: 2484: 2474: 2459: 2181:I like it, but I'd suggest changing this: 2065: 2046: 2033: 2020: 1989: 1970: 1957: 1944: 1931: 1918: 1908: 1897: 1884: 1874: 1864: 1854: 1829: 1819: 1810: 946:It is, it's just not an example we need. 2827:{\displaystyle \{a_{i}\}_{i=0,\dots ,n}} 1651:Because some users might do the formula 1499:being the numeral system we learned with 954:Arithmetic times table unnecessary here. 2958:Knowledge vital articles in Mathematics 2293:) denotes usually the extension to any 1794:Non-standard positional numeral systems 1331:I think we can agree that a digit is a 1310:Positional notation#Digits and numerals 1226:Non-standard positional numeral systems 905:Non-standard positional numeral systems 893:Non-standard positional numeral systems 680:Non-standard positional numeral systems 674:Non-standard positional numeral systems 541: 436: 331: 242: 201: 2973:C-Class vital articles in Mathematics 7: 2983:Mid-importance Anthropology articles 2834:. So far, we have the definition of 1539:represents the numerical value of a 857:IV + XII = V + XI = VI + X = XVI 571:This article is within the scope of 482:This article is within the scope of 377:This article is within the scope of 272:This article is within the scope of 3018:High-importance Typography articles 2572:{\displaystyle b=\mathrm {Hex} =16} 2142:of the digit modifies the meaning: 1773:2A02:A445:EB91:1:A5B6:B3DD:7FE5:9B1 1692:Please let me know what you think. 1474:The paragraph about the meaning of 732:I removed the following paragraph: 704:Category:Positional numeral systems 231:It is of interest to the following 36:for discussing improvements to the 2612:{\displaystyle b=\mathrm {bin} =2} 2599: 2596: 2593: 2559: 2556: 2553: 2382:41216 add last digit =: --> 1894: 1243:List of positional systems by base 292:Knowledge:WikiProject Anthropology 14: 3008:Mid-priority mathematics articles 2381:2576 x 16 =: --> 2380:2576 add next digit =: --> 502:Knowledge:WikiProject Mathematics 295:Template:WikiProject Anthropology 2953:Knowledge level-4 vital articles 2379:161 x 16 =: --> 2378:160 add next digit =: --> 2084:So... what can we do about it?-- 1681: 1657: 682:, and making related changes to 591:Knowledge:WikiProject Typography 564: 543: 505:Template:WikiProject Mathematics 469: 459: 438: 364: 354: 333: 265: 244: 211: 202: 58:Click here to start a new topic. 2993:Low-importance history articles 2260:The Art of Computer Programming 2098:Possible to get inspiration in 1471:The dashes shouldn’t be spaced. 1031:I want to add my base converter 646:Reorganize numeral system stuff 611:This article has been rated as 594:Template:WikiProject Typography 522:This article has been rated as 417:This article has been rated as 312:This article has been rated as 2963:C-Class level-4 vital articles 2893:09:12, 24 September 2020 (UTC) 2878:01:57, 24 September 2020 (UTC) 2408:To me both examples look like 1881: 1812: 1634:04:53, 12 September 2011 (UTC) 1021:03:04, 28 September 2012 (UTC) 982:03:04, 28 September 2012 (UTC) 865:Positional Notation for Base-1 1: 2978:C-Class Anthropology articles 2354:17:10, 20 February 2019 (UTC) 2339:15:49, 20 February 2019 (UTC) 2252:14:50, 20 February 2019 (UTC) 2234:14:17, 20 February 2019 (UTC) 2215:12:31, 20 February 2019 (UTC) 2176:09:37, 20 February 2019 (UTC) 2116:09:44, 20 February 2019 (UTC) 2094:09:04, 20 February 2019 (UTC) 1789:a quite technical definition, 1781:19:22, 19 February 2019 (UTC) 1762:19:56, 13 December 2018 (UTC) 1103:00:05, 12 February 2010 (UTC) 942:00:08, 12 February 2010 (UTC) 719:14:35, 26 February 2006 (UTC) 585:and see a list of open tasks. 496:and see a list of open tasks. 397:Knowledge:WikiProject History 391:and see a list of open tasks. 286:and see a list of open tasks. 55:Put new text under old text. 3003:C-Class mathematics articles 2998:WikiProject History articles 1746:(100) is contained within 伍仟 1261:10:55, 24 October 2010 (UTC) 1210:01:43, 26 January 2010 (UTC) 1172:03:26, 24 January 2010 (UTC) 1144:01:52, 24 January 2010 (UTC) 1128:01:04, 23 January 2010 (UTC) 1084:21:29, 23 January 2010 (UTC) 1065:05:37, 23 January 2010 (UTC) 1049:02:43, 20 January 2010 (UTC) 669:01:58, 6 November 2005 (UTC) 400:Template:WikiProject History 3013:C-Class Typography articles 2933:08:42, 3 October 2022 (UTC) 2914:19:32, 1 October 2022 (UTC) 2299:Hindu–Arabic numeral system 2272:Hindu–Arabic numeral system 961:, and see what they say. — 63:New to Knowledge? Welcome! 3034: 2854:10:08, 6 August 2020 (UTC) 2440:09:27, 6 August 2020 (UTC) 2422:08:57, 6 August 2020 (UTC) 2403:08:31, 6 August 2020 (UTC) 2100:Decimal § Decimal notation 1299:18:53, 24 April 2011 (UTC) 1280:13:27, 26 April 2011 (UTC) 801:17:21, 21 March 2006 (UTC) 788:11:57, 20 March 2006 (UTC) 774:08:51, 20 March 2006 (UTC) 423:project's importance scale 2452:OK, maybe I can help you. 2291:positional numeral system 2268:modern positional systems 1718:11:27, 3 March 2018 (UTC) 1702:23:07, 2 March 2018 (UTC) 1640:a note for Exponentiation 1604:05:54, 14 July 2011 (UTC) 1564:05:54, 14 July 2011 (UTC) 1530:03:12, 14 July 2011 (UTC) 1451:20:54, 25 June 2011 (UTC) 1422:17:50, 22 June 2011 (UTC) 1379:08:23, 22 June 2011 (UTC) 1360:00:46, 22 June 2011 (UTC) 1238:16:59, 13 June 2010 (UTC) 901:Talk:Unary numeral system 728:Mathematical implications 610: 559: 521: 454: 416: 349: 311: 260: 239: 93:Be welcoming to newcomers 22:Skip to table of contents 2988:C-Class history articles 2321:in the digit string. ... 1669:subscript, for example: 923:19:50, 29 May 2009 (UTC) 885:19:33, 29 May 2009 (UTC) 849:17:17, 2 June 2006 (UTC) 655:13:56, 8 Apr 2005 (UTC) 528:project's priority scale 275:WikiProject Anthropology 21: 633: 485:WikiProject Mathematics 2948:C-Class vital articles 2828: 2776:with the coefficients 2770: 2746: 2726: 2613: 2573: 2533: 2075: 1739: 1653:in the incorrect order 1482:is confusing. I think 957:Add to the article on 574:WikiProject Typography 88:avoid personal attacks 2829: 2771: 2747: 2727: 2614: 2574: 2534: 2154:in the digit string. 2076: 1493:One of the sentences 692:Quater-imaginary base 298:Anthropology articles 218:level-4 vital article 113:Neutral point of view 2780: 2760: 2736: 2623: 2583: 2543: 2458: 2287:place-value notation 2132:place-value notation 1809: 1220:I think the section 684:Unary numeral system 508:mathematics articles 118:No original research 2836:positional notation 2732:. Thus, the number 2619:is a shorthand for 2432:Martin of Sheffield 2395:Martin of Sheffield 2346:Martin of Sheffield 2283:Positional notation 2244:Martin of Sheffield 2168:Martin of Sheffield 2128:Positional notation 1913: 1710:Martin of Sheffield 1466:Template talk:ndash 1304:Digits and numerals 908:non-zero number). — 754:transfinite numbers 696:Positional notation 597:Typography articles 380:WikiProject History 38:Positional notation 2824: 2766: 2742: 2722: 2609: 2569: 2529: 2071: 1893: 1461:revision 439021439 746:irrational numbers 700:Base (mathematics) 634:next guy's comment 477:Mathematics portal 227:content assessment 99:dispute resolution 60: 2769:{\displaystyle b} 2745:{\displaystyle A} 1624:comment added by 1329: 1328: 1000:Not convinced. — 921: 903:, especially the 875:comment added by 835: 821:comment added by 758:imaginary numbers 688:Golden ratio base 631: 630: 627: 626: 623: 622: 538: 537: 534: 533: 433: 432: 429: 428: 328: 327: 324: 323: 196: 195: 79:Assume good faith 56: 27: 26: 3025: 2833: 2831: 2830: 2825: 2823: 2822: 2795: 2794: 2775: 2773: 2772: 2767: 2756:in the variable 2751: 2749: 2748: 2743: 2731: 2729: 2728: 2723: 2721: 2720: 2705: 2704: 2686: 2685: 2670: 2669: 2651: 2650: 2641: 2640: 2618: 2616: 2615: 2610: 2602: 2578: 2576: 2575: 2570: 2562: 2538: 2536: 2535: 2530: 2528: 2527: 2518: 2517: 2508: 2507: 2495: 2494: 2479: 2478: 2166:Comments below. 2105: 2080: 2078: 2077: 2072: 2070: 2069: 2051: 2050: 2038: 2037: 2025: 2024: 2000: 1999: 1981: 1980: 1962: 1961: 1949: 1948: 1936: 1935: 1923: 1922: 1912: 1907: 1889: 1888: 1879: 1878: 1869: 1868: 1859: 1858: 1840: 1839: 1824: 1823: 1689: 1685: 1684: 1665: 1661: 1660: 1636: 1596: 1593: 1590: 1587: 1556: 1553: 1550: 1547: 1463: 1443: 1440: 1437: 1434: 1414: 1411: 1408: 1405: 1352: 1349: 1346: 1343: 1315: 1199: 1188:Alfonsine tables 1013: 1010: 1007: 1004: 974: 971: 968: 965: 909: 887: 834: 815: 742:rational numbers 617:importance scale 599: 598: 595: 592: 589: 568: 561: 560: 555: 547: 540: 510: 509: 506: 503: 500: 479: 474: 473: 463: 456: 455: 450: 442: 435: 405: 404: 403:history articles 401: 398: 395: 374: 369: 368: 367: 358: 351: 350: 345: 337: 330: 318:importance scale 300: 299: 296: 293: 290: 269: 262: 261: 256: 248: 241: 224: 215: 214: 207: 206: 198: 192: 191: 177: 108:Article policies 29: 16: 3033: 3032: 3028: 3027: 3026: 3024: 3023: 3022: 2938: 2937: 2901: 2866: 2796: 2786: 2778: 2777: 2758: 2757: 2734: 2733: 2712: 2696: 2671: 2655: 2642: 2632: 2621: 2620: 2581: 2580: 2541: 2540: 2519: 2509: 2499: 2480: 2470: 2456: 2455: 2428:Horner's method 2410:Horner's method 2391: 2384: 2368: 2366:Base conversion 2322: 2164: 2103: 2061: 2042: 2029: 2016: 1985: 1966: 1953: 1940: 1927: 1914: 1880: 1870: 1860: 1850: 1825: 1815: 1807: 1806: 1769: 1740: 1726: 1682: 1680: 1678: 1674: 1658: 1656: 1649: 1642: 1619: 1616: 1594: 1591: 1588: 1585: 1554: 1551: 1548: 1545: 1518:numerical value 1511:in some fonts!” 1488:Numerical digit 1459: 1441: 1438: 1435: 1432: 1412: 1409: 1406: 1403: 1350: 1347: 1344: 1341: 1306: 1287: 1268: 1266:Complex radixes 1245: 1218: 1197: 1111: 1033: 1011: 1008: 1005: 1002: 972: 969: 966: 963: 870: 867: 816: 811: 730: 676: 661: 648: 636: 613:High-importance 596: 593: 590: 587: 586: 554:High‑importance 553: 507: 504: 501: 498: 497: 475: 468: 448: 402: 399: 396: 393: 392: 370: 365: 363: 343: 297: 294: 291: 288: 287: 254: 225:on Knowledge's 222: 212: 134: 129: 128: 127: 104: 74: 12: 11: 5: 3031: 3029: 3021: 3020: 3015: 3010: 3005: 3000: 2995: 2990: 2985: 2980: 2975: 2970: 2965: 2960: 2955: 2950: 2940: 2939: 2936: 2935: 2920: 2900: 2899:Issues Section 2897: 2896: 2895: 2865: 2862: 2861: 2860: 2859: 2858: 2857: 2856: 2842: 2839: 2821: 2818: 2815: 2812: 2809: 2806: 2803: 2799: 2793: 2789: 2785: 2765: 2741: 2719: 2715: 2711: 2708: 2703: 2699: 2695: 2692: 2689: 2684: 2681: 2678: 2674: 2668: 2665: 2662: 2658: 2654: 2649: 2645: 2639: 2635: 2631: 2628: 2608: 2605: 2601: 2598: 2595: 2591: 2588: 2568: 2565: 2561: 2558: 2555: 2551: 2548: 2526: 2522: 2516: 2512: 2506: 2502: 2498: 2493: 2490: 2487: 2483: 2477: 2473: 2469: 2466: 2463: 2453: 2445: 2444: 2443: 2442: 2388: 2376: 2367: 2364: 2363: 2362: 2361: 2360: 2359: 2358: 2357: 2356: 2303:decimal system 2281: 2280: 2279: 2278: 2277: 2276: 2275: 2264: 2237: 2236: 2218: 2217: 2203: 2202: 2201: 2193: 2192: 2191: 2183: 2182: 2126: 2121: 2120: 2119: 2118: 2082: 2068: 2064: 2060: 2057: 2054: 2049: 2045: 2041: 2036: 2032: 2028: 2023: 2019: 2015: 2012: 2009: 2006: 2003: 1998: 1995: 1992: 1988: 1984: 1979: 1976: 1973: 1969: 1965: 1960: 1956: 1952: 1947: 1943: 1939: 1934: 1930: 1926: 1921: 1917: 1911: 1906: 1903: 1900: 1896: 1892: 1887: 1883: 1877: 1873: 1867: 1863: 1857: 1853: 1849: 1846: 1843: 1838: 1835: 1832: 1828: 1822: 1818: 1814: 1802: 1801: 1800: 1797: 1790: 1768: 1765: 1733: 1725: 1722: 1721: 1720: 1679: 1676: 1672: 1647: 1641: 1638: 1615: 1612: 1611: 1610: 1609: 1608: 1607: 1606: 1571: 1570: 1569: 1568: 1567: 1566: 1514: 1513: 1512: 1505: 1502: 1491: 1472: 1427: 1426: 1425: 1424: 1399:overwhelmingly 1366: 1327: 1326: 1323: 1319: 1305: 1302: 1286: 1283: 1267: 1264: 1244: 1241: 1217: 1214: 1213: 1212: 1192: 1191: 1183:Greek numerals 1177: 1176: 1175: 1174: 1157: 1156: 1155: 1154: 1147: 1146: 1110: 1107: 1106: 1105: 1095:Aleph Infinity 1089: 1088: 1087: 1086: 1068: 1067: 1032: 1029: 1028: 1027: 1026: 1025: 1024: 1023: 991: 990: 989: 988: 987: 986: 985: 984: 955: 952: 950:EDITORIALIZING 934:Aleph Infinity 926: 925: 866: 863: 852: 851: 810: 807: 806: 805: 804: 803: 791: 790: 729: 726: 675: 672: 660: 657: 647: 644: 635: 632: 629: 628: 625: 624: 621: 620: 609: 603: 602: 600: 583:the discussion 569: 557: 556: 548: 536: 535: 532: 531: 520: 514: 513: 511: 494:the discussion 481: 480: 464: 452: 451: 443: 431: 430: 427: 426: 419:Low-importance 415: 409: 408: 406: 389:the discussion 376: 375: 372:History portal 359: 347: 346: 344:Low‑importance 338: 326: 325: 322: 321: 314:Mid-importance 310: 304: 303: 301: 284:the discussion 270: 258: 257: 255:Mid‑importance 249: 237: 236: 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2387: 2375: 2372: 2365: 2355: 2351: 2347: 2342: 2341: 2340: 2336: 2332: 2328: 2327: 2326: 2325: 2324: 2323: 2320: 2316: 2314: 2308: 2304: 2300: 2296: 2292: 2288: 2284: 2273: 2269: 2265: 2262: 2261: 2255: 2254: 2253: 2249: 2245: 2241: 2240: 2239: 2238: 2235: 2231: 2227: 2223: 2220: 2219: 2216: 2212: 2208: 2204: 2200: 2197: 2196: 2194: 2190: 2187: 2186: 2185: 2184: 2180: 2179: 2178: 2177: 2173: 2169: 2161: 2159: 2158:decimal point 2153: 2149: 2147: 2141: 2137: 2133: 2129: 2125: 2117: 2113: 2109: 2101: 2097: 2096: 2095: 2091: 2087: 2083: 2066: 2062: 2058: 2055: 2052: 2047: 2043: 2039: 2034: 2030: 2026: 2021: 2017: 2013: 2010: 2007: 2004: 2001: 1996: 1993: 1990: 1986: 1982: 1977: 1974: 1971: 1967: 1963: 1958: 1954: 1950: 1945: 1941: 1937: 1932: 1928: 1924: 1919: 1915: 1909: 1904: 1901: 1898: 1890: 1885: 1875: 1871: 1865: 1861: 1855: 1851: 1847: 1844: 1841: 1836: 1833: 1830: 1826: 1820: 1816: 1803: 1798: 1795: 1791: 1788: 1787: 1785: 1784: 1783: 1782: 1778: 1774: 1766: 1764: 1763: 1759: 1755: 1754:Technotom2001 1751: 1749: 1745: 1738: 1732: 1730: 1729:From § Issues 1723: 1719: 1715: 1711: 1706: 1705: 1704: 1703: 1699: 1695: 1690: 1688: 1670: 1666: 1664: 1654: 1646: 1639: 1637: 1635: 1631: 1627: 1626:96.33.158.121 1623: 1613: 1605: 1602: 1601: 1597: 1582: 1577: 1576: 1575: 1574: 1573: 1572: 1565: 1562: 1561: 1557: 1542: 1538: 1534: 1533: 1531: 1527: 1523: 1519: 1515: 1510: 1506: 1503: 1500: 1496: 1492: 1489: 1485: 1481: 1477: 1473: 1470: 1469: 1467: 1462: 1457: 1456: 1455: 1454: 1453: 1452: 1449: 1448: 1444: 1423: 1420: 1419: 1415: 1400: 1396: 1395: 1390: 1386: 1382: 1381: 1380: 1376: 1372: 1367: 1364: 1363: 1362: 1361: 1358: 1357: 1353: 1336: 1334: 1320: 1316: 1313: 1311: 1303: 1301: 1300: 1296: 1292: 1284: 1282: 1281: 1277: 1273: 1265: 1263: 1262: 1258: 1254: 1250: 1242: 1240: 1239: 1235: 1231: 1227: 1223: 1215: 1211: 1207: 1203: 1194: 1193: 1189: 1184: 1179: 1178: 1173: 1169: 1165: 1161: 1160: 1159: 1158: 1151: 1150: 1149: 1148: 1145: 1141: 1137: 1132: 1131: 1130: 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