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Decimal

The decimal numeral system (also called the base-ten positional numeral system and denary or decanary) is the standard system for denoting integer and non-integer numbers. It is the extension to non-integer numbers (decimal fractions) of the Hindu–Arabic numeral system. The way of denoting numbers in the decimal system is often referred to as decimal notation.

A decimal numeral (also often just decimal or, less correctly, decimal number), refers generally to the notation of a number in the decimal numeral system. Decimals may sometimes be identified by a decimal separator (usually "." or "," as in $25.9703$ or $3,1415$). Decimal may also refer specifically to the digits after the decimal separator, such as in "$3.14$ is the approximation of $\pi$ to two decimals". Zero-digits after a decimal separator serve the purpose of signifying the precision of a value.

The numbers that may be represented in the decimal system are the decimal fractions. That is, fractions of the form $a/10^{n}$, where $a$ is an integer, and $n$ is a non-negative integer. Decimal fractions also result from the addition of an integer and a fractional part; the resulting sum sometimes is called a fractional number.

Decimals are commonly used to approximate real numbers. By increasing the number of digits after the decimal separator, one can make the approximation errors as small as one wants, when one has a method for computing the new digits.

Originally and in most uses, a decimal has only a finite number of digits after the decimal seperator. However, the decimal system has been extended to infinite decimals for representing any real number, by using an infinite sequence of digits after the decimal separator (see decimal representation). In this context, the usual decimals, with a finite number of non-zero digits after the decimal separator, are sometimes called terminating decimals. A repeating decimal is an infinite decimal that, after some place, repeats indefinitely the same sequence of digits (e.g., $5.123144144144144... = 5.123\overline{144}$). An infinite decimal represents a rational number, the quotient of two integers, if and only if it is a repeating decimal or has a finite number of non-zero digits.

Origin
Many numeral systems of ancient civilizations use ten and its powers for representing numbers, possibly because there are ten fingers on two hands and people started counting by using their fingers. Examples are firstly the Egyptian numerals, then the Brahmi numerals, Greek numerals, Hebrew numerals, Roman numerals, and Chinese numerals. Very large numbers were difficult to represent in these old numeral systems, and only the best mathematicians were able to multiply or divide large numbers. These difficulties were completely solved with the introduction of the Hindu–Arabic numeral system for representing integers. This system has been extended to represent some non-integer numbers, called decimal fractions or decimal numbers, for forming the decimal numeral system.

Decimal notation
For writing numbers, the decimal system uses ten decimal digits, a decimal mark, and, for negative numbers, a minus sign "−". The decimal digits are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9; the decimal separator is the dot "$.$" in many countries (mostly English-speaking), and a comma "$,$" in other countries.

For representing a non-negative number, a decimal numeral consists of
 * either a (finite) sequence of digits (such as "2017"), where the entire sequence represents an integer:
 * $$a_ma_{m-1}\ldots a_0$$
 * or a decimal mark separating two sequences of digits (such as "20.70828")
 * $$a_ma_{m-1}\ldots a_0.b_1b_2\ldots b_n$$.

If $m > 0$, that is, if the first sequence contains at least two digits, it is generally assumed that the first digit $a_{m}$ is not zero. In some circumstances it may be useful to have one or more 0's on the left; this does not change the value represented by the decimal: for example, $3.14 = 03.14 = 003.14$. Similarly, if the final digit on the right of the decimal mark is zero—that is, if $b_{n} = 0$—it may be removed; conversely, trailing zeros may be added after the decimal mark without changing the represented number; for example, $15 = 15.0 = 15.00$ and $5.2 = 5.20 = 5.200$.

For representing a negative number, a minus sign is placed before $a_{m}$.

The numeral $$a_ma_{m-1}\ldots a_0.b_1b_2\ldots b_n$$ represents the number
 * $$a_m10^m+a_{m-1}10^{m-1}+\cdots+a_{0}10^0+\frac{b_1}{10^1}+\frac{b_2}{10^2}+\cdots+\frac{b_n}{10^n}$$.

The integer part or integral part of a decimal numeral is the integer written to the left of the decimal separator (see also truncation). For a non-negative decimal numeral, it is the largest integer that is not greater than the decimal. The part from the decimal separator to the right is the fractional part, which equals the difference between the numeral and its integer part.

When the integral part of a numeral is zero, it may occur, typically in computing, that the integer part is not written (for example, $.1234$, instead of $0.1234$). In normal writing, this is generally avoided, because of the risk of confusion between the decimal mark and other punctuation.

In brief, the contribution of each digit to the value of a number depends on its position in the numeral. That is, the decimal system is a positional numeral system.

Decimal fractions
Decimal fractions (sometimes called decimal numbers, especially in contexts involving explicit fractions) are the rational numbers that may be expressed as a fraction whose denominator is a power of ten. For example, the decimal expressions $$0.8, 14.89, 0.00079, 1.618, 3.14159$$ represent the fractions $4⁄5$, $1489⁄100$, $79⁄100000$, $809⁄500$ and $314159⁄100000$, and therefore denote decimal fractions. An example of a fraction that cannot be represented by a decimal expression (with a finite number of digits) is $1⁄3$, 3 not being a power of 10.

More generally, a decimal with $n$ digits after the separator (a point or comma) represents the fraction with denominator $10^{n}$, whose numerator is the integer obtained by removing the separator.

It follows that a number is a decimal fraction if and only if it has a finite decimal representation.

Expressed as fully reduced fractions, the decimal numbers are those whose denominator is a product of a power of 2 and a power of 5. Thus the smallest denominators of decimal numbers are
 * $$1=2^0\cdot 5^0, 2=2^1\cdot 5^0, 4=2^2\cdot 5^0, 5=2^0\cdot 5^1, 8=2^3\cdot 5^0, 10=2^1\cdot 5^1, 16=2^4\cdot 5^0, 20=2^2\cdot5^1, 25=2^0\cdot 5^2, \ldots$$

Approximation using decimal numbers
Decimal numerals do not allow an exact representation for all real numbers. Nevertheless, they allow approximating every real number with any desired accuracy, e.g., the decimal 3.14159 approximates π, being less than 10−5 off; so decimals are widely used in science, engineering and everyday life.

More precisely, for every real number $...5.123$ and every positive integer $x$, there are two decimals $n$ and $L$ with at most $u$ digits after the decimal mark such that $L ≤ x ≤ u$ and $(u − L) = 10^{−n}$.

Numbers are very often obtained as the result of measurement. As measurements are subject to measurement uncertainty with a known upper bound, the result of a measurement is well-represented by a decimal with $n$ digits after the decimal mark, as soon as the absolute measurement error is bounded from above by $10^{−n}$. In practice, measurement results are often given with a certain number of digits after the decimal point, which indicate the error bounds. For example, although 0.080 and 0.08 denote the same number, the decimal numeral 0.080 suggests a measurement with an error less than 0.001, while the numeral 0.08 indicates an absolute error bounded by 0.01. In both cases, the true value of the measured quantity could be, for example, 0.0803 or 0.0796 (see also significant figures).

Infinite decimal expansion
For a real number $n$ and an integer $n ≥ 0$, let $[x]_{n}$ denote the (finite) decimal expansion of the greatest number that is not greater than $x$ that has exactly $x$ digits after the decimal mark. Let $d_{i}$ denote the last digit of $[x]_{i}$. It is straightforward to see that $[x]_{n}$ may be obtained by appending $d_{n}$ to the right of $[x]_{n−1}$. This way one has

and the difference of $[x]_{n} = [x]_{0}.d_{1}d_{2}...d_{n−1}d_{n}$ and $[x]_{n−1}$ amounts to
 * $$\left\vert \left [ x \right ]_n-\left [ x \right ]_{n-1} \right\vert=d_n\cdot10^{-n}<10^{-n+1}$$,

which is either 0, if $[x]_{n}$, or gets arbitrarily small as $n$ tends to infinity. According to the definition of a limit, $n$ is the limit of $d_{n} = 0$ when $x$ tends to infinity. This is written as$\; x = \lim_{n\rightarrow\infty} [x]_n \;$ or

which is called an infinite decimal expansion of $n$.

Conversely, for any integer $[x]_{n}$ and any sequence of digits$\;(d_n)_{n=1}^{\infty}$ the (infinite) expression $x = [x]_{0}.d_{1}d_{2}...d_{n}...$ is an infinite decimal expansion of a real number $x$. This expansion is unique if neither all $[x]_{0}$ are equal to 9 nor all $[x]_{0}.d_{1}d_{2}...d_{n}...$ are equal to 0 for $x$ large enough (for all $n$ greater than some natural number $n$).

If all $d_{n}$ for $d_{n}$ equal to 9 and $d_{n}$, the limit of the sequence$\;([x]_n)_{n=1}^{\infty}$ is the decimal fraction obtained by replacing the last digit that is not a 9, i.e.: $n > N$, by $[x]_{n} = [x]_{0}.d_{1}d_{2}...d_{n}$, and replacing all subsequent 9s by 0s (see 0.999...).

Any such decimal fraction, i.e.: $d_{N}$ for $d_{N} + 1$, may be converted to its equivalent infinite decimal expansion by replacing $d_{n} = 0$ by $n > N$ and replacing all subsequent 0s by 9s (see 0.999...).

In summary, every real number that is not a decimal fraction has a unique infinite decimal expansion. Each decimal fraction has exactly two infinite decimal expansions, one containing only 0s after some place, which is obtained by the above definition of $d_{N}$, and the other containing only 9s after some place, which is obtained by defining $d_{N} − 1$ as the greatest number that is less than $N$, having exactly $x$ digits after the decimal mark.

Rational numbers
Long division allows computing the infinite decimal expansion of a rational number. If the rational number is a decimal fraction, the division stops eventually, producing a decimal numeral, which may be prolongated into an infinite expansion by adding infinitely many zeros. If the rational number is not a decimal fraction, the division may continue indefinitely. However, as all successive remainders are less than the divisor, there are only a finite number of possible remainders, and after some place, the same sequence of digits must be repeated indefinitely in the quotient. That is, one has a repeating decimal. For example,
 * $n$ = 0. 012345679 012... (with the group 012345679 indefinitely repeating).

The converse is also true: if, at some point in the decimal representation of a number, the same string of digits starts repeating indefinitely, the number is rational. or, dividing both numerator and denominator by 6, $1⁄81$.

Decimal computation

Most modern computer hardware and software systems commonly use a binary representation internally (although many early computers, such as the ENIAC or the IBM 650, used decimal representation internally). For external use by computer specialists, this binary representation is sometimes presented in the related octal or hexadecimal systems.

For most purposes, however, binary values are converted to or from the equivalent decimal values for presentation to or input from humans; computer programs express literals in decimal by default. (123.1, for example, is written as such in a computer program, even though many computer languages are unable to encode that number precisely.)

Both computer hardware and software also use internal representations which are effectively decimal for storing decimal values and doing arithmetic. Often this arithmetic is done on data which are encoded using some variant of binary-coded decimal, especially in database implementations, but there are other decimal representations in use (including decimal floating point such as in newer revisions of the IEEE 754 Standard for Floating-Point Arithmetic).

Decimal arithmetic is used in computers so that decimal fractional results of adding (or subtracting) values with a fixed length of their fractional part always are computed to this same length of precision. This is especially important for financial calculations, e.g., requiring in their results integer multiples of the smallest currency unit for book keeping purposes. This is not possible in binary, because the negative powers of $$10$$ have no finite binary fractional representation; and is generally impossible for multiplication (or division). See Arbitrary-precision arithmetic for exact calculations.

History
Many ancient cultures calculated with numerals based on ten, perhaps because two human hands have ten fingers. Standardized weights used in the Indus Valley Civilisation (c. 3300–1300 BCE) were based on the ratios: 1/20, 1/10, 1/5, 1/2, 1, 2, 5, 10, 20, 50, 100, 200, and 500, while their standardized ruler – the Mohenjo-daro ruler – was divided into ten equal parts. Egyptian hieroglyphs, in evidence since around 3000 BCE, used a purely decimal system, as did the Linear A script (c. 1800–1450 BCE) of the Minoans and the Linear B script (c. 1400–1200 BCE) of the Mycenaeans. The Únětice culture in central Europe (2300-1600 BC) used standardised weights and a decimal system in trade. The number system of classical Greece also used powers of ten, including an intermediate base of 5, as did Roman numerals. Notably, the polymath Archimedes (c. 287–212 BCE) invented a decimal positional system in his Sand Reckoner which was based on 108. Hittite hieroglyphs (since 15th century BCE) were also strictly decimal.

The Egyptian hieratic numerals, the Greek alphabet numerals, the Hebrew alphabet numerals, the Roman numerals, the Chinese numerals and early Indian Brahmi numerals are all non-positional decimal systems, and required large numbers of symbols. For instance, Egyptian numerals used different symbols for 10, 20 to 90, 100, 200 to 900, 1000, 2000, 3000, 4000, to 10,000. The world's earliest positional decimal system was the Chinese rod calculus.

History of decimal fractions
Starting from the 2nd century BCE, some Chinese units for length were based on divisions into ten; by the 3rd century CE these metrological units were used to express decimal fractions of lengths, non-positionally. Calculations with decimal fractions of lengths were performed using positional counting rods, as described in the 3rd–5th century CE Sunzi Suanjing. The 5th century CE mathematician Zu Chongzhi calculated a 7-digit approximation of $4152⁄9990$. Qin Jiushao's book Mathematical Treatise in Nine Sections (1247) explicitly writes a decimal fraction representing a number rather than a measurement, using counting rods. The number 0.96644 is denoted

 * 寸
 * Counting rod 0.png Counting rod h9 num.png Counting rod v6.png Counting rod h6.png Counting rod v4.png Counting rod h4.png.

Historians of Chinese science have speculated that the idea of decimal fractions may have been transmitted from China to the Middle East.

Al-Khwarizmi introduced fractions to Islamic countries in the early 9th century CE, written with a numerator above and denominator below, without a horizontal bar. This form of fraction remained in use for centuries.

Positional decimal fractions appear for the first time in a book by the Arab mathematician Abu'l-Hasan al-Uqlidisi written in the 10th century. The Jewish mathematician Immanuel Bonfils used decimal fractions around 1350 but did not develop any notation to represent them. The Persian mathematician Jamshid al-Kashi used, and claimed to have discovered, decimal fractions in the 15th century.

A forerunner of modern European decimal notation was introduced by Simon Stevin in the 16th century. Stevin's influential booklet De Thiende ("the art of tenths") was first published in Dutch in 1585 and translated into French as La Disme.

John Napier introduced using the period (.) to separate the integer part of a decimal number from the fractional part in his book on constructing tables of logarithms, published posthumously in 1620.

Natural languages
A method of expressing every possible natural number using a set of ten symbols emerged in India. Several Indian languages show a straightforward decimal system. Dravidian languages have numbers between 10 and 20 expressed in a regular pattern of addition to 10.

The Hungarian language also uses a straightforward decimal system. All numbers between 10 and 20 are formed regularly (e.g. 11 is expressed as "tizenegy" literally "one on ten"), as with those between 20 and 100 (23 as "huszonhárom" = "three on twenty").

A straightforward decimal rank system with a word for each order (10 十, 100 百, 1000 千, 10,000 万), and in which 11 is expressed as ten-one and 23 as two-ten-three, and 89,345 is expressed as 8 (ten thousands) 万 9 (thousand) 千 3 (hundred) 百 4 (tens) 十 5 is found in Chinese, and in Vietnamese with a few irregularities. Japanese, Korean, and Thai have imported the Chinese decimal system. Many other languages with a decimal system have special words for the numbers between 10 and 20, and decades. For example, in English 11 is "eleven" not "ten-one" or "one-teen".

Incan languages such as Quechua and Aymara have an almost straightforward decimal system, in which 11 is expressed as ten with one and 23 as two-ten with three.

Some psychologists suggest irregularities of the English names of numerals may hinder children's counting ability.

Other bases
Some cultures do, or did, use other bases of numbers.
 * Pre-Columbian Mesoamerican cultures such as the Maya used a base-20 system (perhaps based on using all twenty fingers and toes).
 * The Yuki language in California and the Pamean languages in Mexico have octal (base-8) systems because the speakers count using the spaces between their fingers rather than the fingers themselves.
 * The existence of a non-decimal base in the earliest traces of the Germanic languages is attested by the presence of words and glosses meaning that the count is in decimal (cognates to "ten-count" or "tenty-wise"); such would be expected if normal counting is not decimal, and unusual if it were.  Where this counting system is known, it is based on the "long hundred" = 120, and a "long thousand" of 1200. The descriptions like "long" only appear after the "small hundred" of 100 appeared with the Christians. Gordon's Introduction to Old Norse  p. 293, gives number names that belong to this system. An expression cognate to 'one hundred and eighty' translates to 200, and the cognate to 'two hundred' translates to 240. Goodare details the use of the long hundred in Scotland in the Middle Ages, giving examples such as calculations where the carry implies i C (i.e. one hundred) as 120, etc. That the general population were not alarmed to encounter such numbers suggests common enough use. It is also possible to avoid hundred-like numbers by using intermediate units, such as stones and pounds, rather than a long count of pounds. Goodare gives examples of numbers like vii score, where one avoids the hundred by using extended scores. There is also a paper by W.H. Stevenson, on 'Long Hundred and its uses in England'.
 * Many or all of the Chumashan languages originally used a base-4 counting system, in which the names for numbers were structured according to multiples of 4 and 16.
 * Many languages use quinary (base-5) number systems, including Gumatj, Nunggubuyu, Kuurn Kopan Noot and Saraveca. Of these, Gumatj is the only true 5–25 language known, in which 25 is the higher group of 5.
 * Some Nigerians use duodecimal systems. So did some small communities in India and Nepal, as indicated by their languages.
 * The Huli language of Papua New Guinea is reported to have base-15 numbers. Ngui means 15, ngui ki means 15 × 2 = 30, and ngui ngui means 15 × 15 = 225.
 * Umbu-Ungu, also known as Kakoli, is reported to have base-24 numbers. Tokapu means 24, tokapu talu means 24 × 2 = 48, and tokapu tokapu means 24 × 24 = 576.
 * Ngiti is reported to have a base-32 number system with base-4 cycles.
 * The Ndom language of Papua New Guinea is reported to have base-6 numerals. Mer means 6, mer an thef means 6 × 2 = 12, nif means 36, and nif thef means 36×2 = 72.

title: Decimal


text:
Talk:Decimal

Consider adding to Intro
Consider adding the following text to the intro of the article, as discussing the limitations of the base 10 system would be beneficial for readers curious about such information regarding it. The text is in brackets. [Though the decimal (base 10) system is widely used, it is not free of criticism. As 10 is only divisible by itself, 1, 2, and 5, proponents of other base number systems (such as base 12) would argue that using a base number with more factors would make math simpler (as 3, 4, and 6 go perfectly into a dozen). (see https://en.wikipedia.org/wiki/Duodecimal)]
 * This article is about the decimal base, not about the comparison of bases, which is the subject of the article Number base. Moreover, your formulation is not convenient for an encyclopedia; for a convenient tone, see the dozenal entry in the table in . D.Lazard (talk) 13:58, 28 April 2022 (UTC)

 * I see your point, and thanks for informing me. Disregard the edit suggestion. 104.35.147.45 (talk) 22:42, 28 April 2022 (UTC)

Add subsection on conversion
I suggest to add a subsection on conversion to numbers with different bases AXO NOV  (talk) ⚑ 15:17, 28 May 2023 (UTC)

Decimals in the Vedas
Sorry, I overlooked your "fv" edit summary here. If you've checked the Atharva Veda and it doesn't support the claim, tagging the reference with Failed verification would be appropriate, but IMHO deleting the paragraph is too radical. Peter Brown (talk) 22:39, 11 June 2023 (UTC)

 * Hi. Yes, I did check it. It's a primary source, actually, of a hymn. I did search google books/scholar for "Atharvaveda" + decimal fractions (with and without a space in "Atharva Veda") and it turned up nothing beyond a couple of references to place value (related to the text having words for the numbers 10^4, 10^8, and so on). A google search of the specific citation turns up Hindu twitter accounts and websites, and nothing scholarly. This exact citation was, I believe, copied directly from "Hindupedia", although that page does not really assert what this sentence asserts. Certainly none of it appears to support the statement that the text makes use of "mathematical decimal fractions", which also conflicts with the information in this article, which puts the first use of decimal fractions around a thousand years after that. But I do not feel strongly enough about it to undo your reversion. Dragoon17 (talk) 04:46, 12 June 2023 (UTC)
 * I have deleted it as it comes under WP:NOR. അദ്വൈതൻ (talk) 22:05, 8 July 2024 (UTC)

"Generally", "usual"
I have some concerns about this text:
 * "Generally, a decimal has only a finite number of digits after the decimal seperator. However, the decimal system has been extended to infinite decimals for representing any real number, by using an infinite sequence of digits after the decimal separator (see decimal representation). In this context, the usual decimals, with a finite number of non-zero digits after the decimal separator, are sometimes called terminating decimals."

Where does this "generally" come from? I think the most common usage is actually as an approximation to some measured quantity. For example this desk is 90.2 centimeters wide means something like "I can measure the desk's width to a precision of roughly 0.1 cm, and when I do that it comes out 90.2. It's probably between 90.15 and 90.25, but I'm not signing over my firstborn in case it's a little outside that range."

Now, to the extent that the desk's width is completely well-defined (which of course it probably isn't, but let's go with it for now), if you had better and better measurement tools, you could keep going, adding more and more digits, without any obvious fixed limit.

So "generally" there's no actual fixed finite number of digits to which a decimal should be expanded. The exception would be if you had some reason to believe the exact answer were of the form $$\tfrac{n}{10^m}$$ for some natural numbers $$n$$ and $$m$$, which is almost never the case.

That's in the "real-life" case. In mathematics, for representing real numbers, actually all decimal expansions are infinite; it's just that some eventually start spitting out the value 0 and never stop.

Not sure how best to fix this; it is good to have somewhere to point terminating decimal, as ultimately unimportant as the concept is. --Trovatore (talk) 01:08, 15 January 2024 (UTC)

 * IMO, it suffices to replace "Generally" with "Originally and in most uses". Even in mathematics, infinite decimals are not really used, except for the study of the cardinality of the real numbers. I agree that "Generally" is confusing, as if may be wrongly understood as "most decimals are finite". D.Lazard (talk) 08:35, 15 January 2024 (UTC)
 * I actually think the first sentence should just be removed, and the second sentence should not talk of an "extension" but rather should say that the expansion may be infinite. Then the third sentence should change to saying that a "terminating decimal" is one that can be expressed with a finite number of digits (of course it isn't really finite, it just starts becoming all zeroes, but we can leave that out in this spot). --Trovatore (talk) 20:40, 15 January 2024 (UTC)
 * I strongly oppose to your suggestion. Basically, a (finite) decimal is a numeral that allows representing some numbers, namely the decimal fractions. Infinite decimals are not numerals, as most of them cannot be written; they may be viewed as increasing sequences or series, and have a very different nature. Finite decimals were known in Westerm Europe since Fibonacci, while the formal definition of an infinite decimal requires actual infinity. So, saying that infinite decimals are an extension of finite decimals is coherent with history and with the level of abstraction needed to understand the concepts. Saying, as you suggest, that finite decimals are only a special case of infinite decimals, is logically correct, but, IMO, a form of pedantry, consisting of asking the reader to understand complicate things before using more simpler and more useful things. D.Lazard (talk) 21:53, 15 January 2024 (UTC)
 * The thing is, the finite decimals are not about representing numbers exactly (and since you brought up history, they never have been about representing numbers exactly). They're about representing numbers approximately.  The only ones they can represent exactly are those rationals with a denominator whose only prime factors are 2 and 5, which is not a particularly interesting class of numbers in either mathematics or science (oh, I expect there's some interesting mathematics you can do with them, but whatever it is, I doubt it's very relevant to this discussion).
 * So I think it's misleading (and by the way unsourced) to call out the finite decimals as a special class. It's particularly dangerous given that many readers of this article are already foggy on the difference between numbers and numerals, and already think there's something special about base 10.
 * My suggestion is not intended to add pedantry; it's mostly about removing language that I think is currently problematic. I'm happy to rethink it to avoid any active suggestion that the finite decimals are a special case.  I just don't think we should walk readers down a garden path towards the idea that they're the main case. --Trovatore (talk) 22:21, 15 January 2024 (UTC)
 * Nobody is saying that finite decimals represent all numbers exactly. They represent decimal fractions exacly, and are widely used to approximate real numbers. Infinite decimals are essentially used only for the study of the cardinality of the continuum. So the main case is definitively the finite case, except possibly for specialists of mathematical logic. IMHO, infinite decimals should not be taught before college. In any case, they should not be taught to people who do not master approximations. D.Lazard (talk) 22:42, 15 January 2024 (UTC)
 * For precision you should say something like "decadic fraction" rather than decimal fraction, as an infinite decimal arguably is a "decimal fraction". ("Fraction" here is in the sense of part of something, not in the sense of ratio of integers.)
 * It's true that finite decimals represent decadic fractions exactly, but those are fairly unimportant and definitely not the motivation for the notation.
 * One test example: We should probably point out early that 2.3 means something different from 2.30, as the latter implies higher precision.
 * I am not suggesting that we should lead heavily with infinite decimals. I do think we should remove the language that I've called out. --Trovatore (talk) 22:50, 15 January 2024 (UTC)
 * you should say something like "decadic fraction" – in your own textbook you can make up whatever neologism you like. Wikipedia should stick to standard terminology where it exists (and in the rare exceptional case where a non-standard term is needed for whatever reason, should be extremely clear to point that out).
 * finite decimals [are] unimportant and definitely not the motivation for the notation – what does this mean? Which notation are you referring to? –jacobolus (t) 23:51, 15 January 2024 (UTC)
 * I wasn't suggesting that we should add that term to the article. I was pointing out that the term "decimal fraction" does not in itself capture the restriction to finite decimals, and proposing a term D.Lazard could have used in this discussion.
 * Also I didn't say finite decimals were unimportant. What I said, or at least what I meant, is that the numbers exactly represented by finite decimals (the ones of the form $$\tfrac{n}{10^m}$$) are unimportant (as a class), and irrelevant to the motivation for decimal-fraction notation. --Trovatore (talk) 00:25, 16 January 2024 (UTC)
 * A couple more remarks: Your claims about the limited applications that infinite decimals are "used" for seem to apply only to actually infinite decimal expansions.  Potentially infinite expansions have been known much longer, and schoolchildren are familiar with the idea that you can do decimal division of 1 by 3 and it keeps spitting out 3s, and the more advanced ones will know that there's an algorithm for computing (say) $$\sqrt{2}$$, and it will keep spitting out digits without ever settling into a fixed repetitive pattern.
 * This language that emphasizes finite decimal expansions seems to exclude even this rather basic piece of knowledge.
 * But surely we don't want to go onto a digression about actual versus potential infinity, certainly not in the lead, and probably not in this article at all. It's an almost Scholastic distinction that has little to do with the topic given by the title. --Trovatore (talk) 23:10, 15 January 2024 (UTC)
 * But surely we don't want to go onto a digression about actual versus potential infinity, certainly not in the lead, and probably not in this article at all. It's an almost Scholastic distinction that has little to do with the topic given by the title. --Trovatore (talk) 23:10, 15 January 2024 (UTC)

redirect from "base 10"
"base 10" might as well be binary, seximal, octal, dozenal or almost any other base perhaps there should be a redir, something like ''"Base 10" redirects here. For other uses, see List of numeral systems.''? Pandaqwanda (talk) 09:58, 17 February 2024 (UTC)

 * Base 10 redirects to Decimal; base 8 redirects to Octal; base 6 redirects to Senary; base 12 redirects to Duodecimal; base 16 redirects to Hexadecimal. Template redir is useful only for ambiguous redirects. This is not the case here. D.Lazard (talk) 10:19, 17 February 2024 (UTC)
 * i started the topic because, in the context of numeral systems, there isn't really such a thing as "base 10". in almost all bases, "10" is how you write the base itself: it can be two and hence base 10 can be binary, it can be five and hence base 10 can be quinary, etc also, the page in question seemingly doesn't refer to decimal as "base 10" anywherePandaqwanda (talk) 13:11, 17 February 2024 (UTC)
 * In English, when 10 is written without other specification, this means the number ten, not the numeral representing another number in another base. It is true that 10 is a numeral that represents a base in the base itself. It seems that you confuse "numeral 10" with "base 10". D.Lazard (talk) 14:07, 17 February 2024 (UTC)
 * i see, nevermind then. consensus: keep the redirect. Pandaqwanda (talk) 14:58, 17 February 2024 (UTC) (edited the resolved to lowercase Pandaqwanda (talk) 15:09, 17 February 2024 (UTC)) (edited the resolved to say "resolved" instead of "redirect", mixed up words at the time pandaqwanda (talk) 08:41, 19 February 2024 (UTC))

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Talk:Decimal


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Dorians

The Dorians (Δωριεῖς, Dōrieîs, singular Δωριεύς, Dōrieús) were one of the four major ethnic groups into which the Hellenes (or Greeks) of Classical Greece divided themselves (along with the Aeolians, Achaeans, and Ionians). They are almost always referred to as just "the Dorians", as they are called in the earliest literary mention of them in the Odyssey, where they already can be found inhabiting the island of Crete.

They were diverse in way of life and social organization, varying from the populous trade center of the city of Corinth, known for its ornate style in art and architecture, to the isolationist, military state of Sparta; and yet, all Hellenes knew which localities were Dorian and which were not. Dorian states at war could more likely, but not always, count on the assistance of other Dorian states. Dorians were distinguished by the Doric Greek dialect and by characteristic social and historical traditions.

In the 5th century BC, Dorians and Ionians were the two most politically important Greek ethnē, whose ultimate clash resulted in the Peloponnesian War. The degree to which fifth-century Hellenes self-identified as "Ionian" or "Dorian" has itself been disputed. At one extreme Édouard Will concludes that there was no true ethnic component in fifth-century Greek culture, in spite of anti-Dorian elements in Athenian propaganda. At the other extreme John Alty reinterprets the sources to conclude that ethnicity did motivate fifth-century actions. Moderns viewing these ethnic identifications through the 5th and 4th century BC literary tradition have been profoundly influenced by their own social politics. Also, according to E. N. Tigerstedt, nineteenth-century European admirers of virtues they considered "Dorian" identified themselves as "Laconophile" and found responsive parallels in the culture of their day as well; their biases contribute to the traditional modern interpretation of "Dorians".

Origin
Accounts vary as to the Dorians' place of origin. One theory, widely believed in ancient times, is that they originated in the mountainous regions of Greece, such as Macedonia and Epirus, and obscure circumstances brought them south into the Peloponnese, to certain Aegean islands.

Peloponnesian dialect replacement
The origin of the Dorians is a multifaceted concept. In modern scholarship, the term has often meant the location of the population disseminating the Doric Greek dialect within a hypothetical Proto-Greek speaking population. The dialect is known from records of classical northwestern Greece, the Peloponnesus and Crete and some of the islands. The geographic and ethnic information found in the west's earliest known literary work, the Iliad, combined with the administrative records of the former Mycenaean states, prove to universal satisfaction that East Greek (Ionian) speakers were once dominant in the Peloponnesus but suffered a setback there and were replaced at least in official circles by West Greek (Doric) speakers. An historical event is associated with the overthrow, called anciently the Return of the Heracleidai and by moderns the Dorian Invasion.

This theory of a return or invasion presupposes that West Greek speakers resided in northwest Greece but overran the Peloponnesus replacing the East Greek there with their own dialect. No records other than Mycenaean ones are known to have existed in the Bronze Age so a West Greek of that time and place can be neither proved nor disproved. West Greek speakers were in western Greece in classical times. Unlike the East Greeks, they are not associated with any evidence of displacement events. That provides circumstantial evidence that the Doric dialect disseminated among the Hellenes of northwest Greece, a highly-mountainous and somewhat-isolated region.

Dorian invasion
The Dorian invasion is a modern historical concept attempting to account for:
 * at least the replacement of dialects and traditions in southern Greece in pre-classical times
 * more generally, the distribution of the Dorians in Classical Greece
 * the presence of the Dorians in Greece at all

On the whole, none of the objectives has been met, but the investigations served to rule out various speculative hypotheses. Most scholars doubt that the Dorian invasion was the main cause of the collapse of the Mycenaean civilization. The source of the West Greek speakers in the Peloponnese remains unattested by any solid evidence.

Post-migrational distribution of the Dorians
Though most of the Dorians settled in the Peloponnese, they also settled on Rhodes and Sicily and in what is now Southern Italy. In Asia Minor existed the Dorian Hexapolis (the six great Dorian cities): Halikarnassos (Halicarnassus) and Knidos (Cnidus) in Asia Minor, Kos, and Lindos, Kameiros, and Ialyssos on the island of Rhodes. The six cities would later become rivals with the Ionian cities of Asia Minor. The Dorians also settled Crete. The origin traditions remained strong into classical times: Thucydides saw the Peloponnesian War in part as "Ionians fighting against Dorians" and reported the tradition that the Syracusans in Sicily were of Dorian descent. Other such "Dorian" colonies, originally from Corinth, Megara, and the Dorian islands, dotted the southern coasts of Sicily from Syracuse to Selinus. Also Taras was a Spartan colony.

Dorian of Bronze Age Pylos
A man's name, Dōrieus, occurs in the Linear B tablets at Pylos, one of the regions later invaded and subjugated by the Dorians. Pylos tablet Fn867 records it in the dative case as do-ri-je-we, *Dōriēwei, a third- or consonant-declension noun with stem ending in w. An unattested nominative plural, *Dōriēwes, would have become Dōrieis by loss of the w and contraction. The tablet records the grain rations issued to the servants of "religious dignitaries" celebrating a religious festival of Potnia, the mother goddess.

The nominative singular, Dōrieus, remained the same in the classical period. Many Linear B names of servants were formed from their home territory or the places where they came into Mycenaean ownership. Carl Darling Buck sees the -eus suffix as very productive. One of its uses was to convert a toponym to an anthroponym; for example, Megareus, "Megarian", from Megara. A Dōrieus would be from Dōris, the only classical Greek state to serve as the basis for the name of the Dorians. The state was a small one in the mountains of west central Greece. However, classical Doris may not have been the same as Mycenaean Doris.

Dorians of upland Doris
A number of credible etymologies by noted scholars have been proposed. Julius Pokorny derives Δωριεύς, Dōrieus from δωρίς, dōris, "woodland" (which can also mean upland). The dōri- segment is from the o-grade (either ō or o) of Proto-Indo-European *deru-, "tree", which also gives the Homeric Δούρειος Ἵππος (Doureios Hippos, "Wooden Horse"). This derivation has the advantage of naming the people after their wooded, mountainous country.

Lancers
A second popular derivation was given by the French linguist, Émile Boisacq, from the same root, but from Greek δόρυ (doru) 'spear-shaft' (which was made of wood); i.e., "the people of the spear" or "spearmen." In this case the country would be named after the people, as in Saxony from the Saxons. However, R. S. P. Beekes doubted the validity of this derivation and asserted that no good etymology exists.

Chosen Greeks
It sometimes happens that different derivations of an Indo-European word exploit similar-sounding Indo-European roots. Greek doru, "lance," is from the o-grade of Indo-European *deru, "solid," in the sense of wood. It is similar to an extended form, *dō-ro-, of *dō-, (give), as can be seen in the modern Greek imperative δώσε (dose, "give [sing.]!") appearing in Greek as δῶρον (dōron, "gift"). This is the path taken by Jonathan Hall, relying on elements taken from the myth of the Return of the Herakleidai.

Hall cites the tradition, based on a fragment of the poet, Tyrtaeus, that "Sparta is a divine gift granted by Zeus and Hera" to the Heracleidae. In another version, Tyndareus gives his kingdom to Heracles in gratitude for restoring him to the throne, but Heracles "asks the Spartan king to safeguard the gift until his descendants might claim it."

Hall, therefore, proposes that the Dorians are the people of the gift. They assumed the name on taking possession of Lacedaemon. Doris was subsequently named after them. Hall makes comparisons of Spartans to Hebrews as a chosen people maintaining a covenant with God and being assigned a Holy Land. To arrive at this conclusion, Hall relies on Herodotus' version of the myth (see below) that the Hellenes under Dorus did not take his name until reaching the Peloponnesus. In other versions the Heracleidae enlisted the help of their Dorian neighbors. Hall does not address the problem of the Dorians not calling Lacedaemon Doris, but assigning that name to some less holy and remoter land. Similarly, he does not mention the Dorian servant at Pylos, whose sacred gift, if such it was, was still being ruled by the Achaean Atreid family at Lacedaemon.

A minor, and perhaps regrettably forgotten, episode in the history of scholarship was the attempt to emphasize the etymology of Doron with the meaning of 'hand'. This in turn was connected to an interpretation of the famous lambda on Spartan shields, which was to rather stand for a hand with outstanding thumb than the initial letter of Lacedaimon. Given the origin of the Spartan shield lambda legend, however, in a fragment by Eupolis, an Athenian comic poet, there has been a recent attempt to suggest that a comic confusion between the letter and the hand image may yet have been intended.

Social structure
Dorian social structure was characterized by a communal social structure and separation of the sexes. The lives of free men centered around military campaigns. When not abroad, men stayed in all-male residences focusing on military training until the age of 30, regardless of marital status.

Dorian women had greater freedom and economic power than women of other Greek ethnicities. Unlike other Hellenic women, Dorian women were able to own property, manage their husbands' estate, and delegate many domestic tasks to slaves. Women in ancient Sparta possessed the greatest agency and economic power, likely due to the prolonged absences of men during military campaigns. Dorian women wore the peplos, which was once common to all Hellenes. This tunic was pinned at the shoulders by brooches and had slit skirts which bared the thighs and permitted more freedom of movement than the voluminous Ionian chiton (costume).

Distinctions of language
The Doric dialect was spoken in northwest Greece, the Peloponnese, Crete, southwest Asia Minor, the southernmost islands of the Aegean Sea, and the various Dorian colonies of Magna Graecia in Southern Italy and Sicily. After the classical period, it was mainly replaced by the Attic dialect upon which the Koine or "common" Greek language of the Hellenistic period was based. The main characteristic of Doric was the preservation of Proto-Indo-European, long $⟨α⟩$, which in Attic-Ionic became , $⟨η⟩$. A famous example is the valedictory phrase uttered by Spartan mothers to their sons before sending them off to war: ἢ τὰν ἢ ἐπὶ τᾶς (ḕ tàn ḕ epì tâs, literally "either with it or on it": return alive with your shield or dead upon it) would have been ἢ τὴν ἢ ἐπὶ τῆς (ḕ tḕn ḕ epì tês) in the Attic-Ionic dialect of an Athenian mother. Tsakonian, a descendant of Doric Greek, is still spoken in some parts of the southern Argolid coast of the Peloponnese, in the modern prefecture of Arcadia.

Other cultural distinctions
Culturally, in addition to their Doric dialect of Greek, Doric colonies retained their characteristic Doric calendar that revolved round a cycle of festivals, the Hyacinthia and the Carneia being especially important.

The Dorian mode in music also was attributed to Doric societies and was associated by classical writers with martial qualities.

The Doric order of architecture in the tradition inherited by Vitruvius included the Doric column, noted for its simplicity and strength.

The Dorians seem to have offered the central mainland cultus for Helios. The scattering of cults of the sun god in Sicyon, Argos, Ermioni, Epidaurus and Laconia, and his holy livestock flocks at Taenarum, seem to suggest that the deity was considerably important in Dorian religion, compared to other parts of ancient Greece. Additionally, it may have been the Dorians to import his worship to Rhodes.

Ancient traditions
In Greek historiography, the Dorians are mentioned by many authors. The chief classical authors to relate their origins are Herodotus, Thucydides and Pausanias. The most copious authors, however, lived in Hellenistic and Roman times, long after the main events. This apparent paradox does not necessarily discredit the later writers, who were relying on earlier works that did not survive. The customs of the Spartan state and its illustrious individuals are detailed at great length in such authors as Plutarch and Diodorus Siculus.

Homer
The Odyssey has one reference to the Dorians: "There is a land called Crete, in the midst of the wine-dark sea, a fair, rich land, begirt with water, and therein are many men, past counting, and ninety cities. They have not all the same speech, but their tongues are mixed. There dwell Achaeans, there great-hearted native Cretans, there Cydonians, and Dorians of waving plumes, and goodly Pelasgians." The reference is not compatible with a Dorian invasion that brought Dorians to Crete only after the fall of the Mycenaean states. In the Odyssey, Odysseus and his relatives visit those states. Two solutions are possible, either the Odyssey is anachronistic or Dorians were on Crete in Mycenaean times. The uncertain nature of the Dorian invasion defers a definitive answer until more is known about it. Also, the Messenian town of Dorium is mentioned in the Catalogue of Ships. If its name comes from Dorians, it would imply there were settlements of the latter in Messenia during that time as well.

Tyrtaeus
Tyrtaeus, a Spartan poet, became advisor of the Lacedaemonians in their mid-7th-century war to suppress a rebellion of the Messenians. The latter were a remnant of the Achaeans conquered "two generations before", which suggests a rise to supremacy at the end of the Dark Age rather than during and after the fall of Mycenae. The Messenian population was reduced to serfdom.

Only a few fragments of Tyrtaeus' five books of martial verse survive. His is the earliest mention of the three Dorian tribes: Pamphyli, Hylleis, Dymanes. He also says:

"For Cronus' Son Himself, Zeus the husband of fair-crowned Hera, hath given this city to the children of Heracles, with whom we came into the wide isle of Pelops from windy Erineus."

Erineus was a village of Doris. He helped to establish the Spartan constitution, giving the kings and elders, among other powers, the power to dismiss the assembly. He established a rigorous military training program for the young including songs and poems he wrote himself, such as the "Embateria or Songs of the Battle-Charge which are also called Enoplia or Songs-under-Arms". These were chants used to establish the timing of standard drills under arms. He stressed patriotism:

"For 'tis a fair thing for a good man to fall and die fighting in the van for his native land, ... let us fight with a will for this land, and die for our children and never spare our lives."

Herodotus

Herodotus was from Halicarnassus, a Dorian colony on the southwest coast of Asia Minor; following the literary tradition of the times he wrote in Ionic Greek, being one of the last authors to do so. He described the Persian Wars, giving a thumbnail account of the histories of the antagonists, Greeks and Persians.

Herodotus gives a general account of the events termed "the Dorian Invasion", presenting them as transfers of population. Their original home was in Thessaly, central Greece. He goes on to expand in mythological terms, giving some of the geographic details of the myth: 1.56.2-3 And inquiring he found that the Lacedemonians and the Athenians had the pre-eminence, the first of the Dorian and the others of the Ionian race. For these were the most eminent races in ancient time, the second being a Pelasgian and the first a Hellenic race: and the one never migrated from its place in any direction, while the other was very exceedingly given to wanderings; for in the reign of Deucalion this race dwelt in Pthiotis, and in the time of Doros the son of Hellen in the land lying below Ossa and Olympos, which is called Histiaiotis; and when it was driven from Histiaiotis by the sons of Cadmos, it dwelt in Pindos and was called Makednian; and thence it moved afterwards to Dryopis, and from Dryopis it came finally to Peloponnesus, and began to be called Dorian.

1.57.1-3 What language however the Pelasgians used to speak I am not able with certainty to say. But if one must pronounce judging by those that still remain of the Pelasgians who dwelt in the city of Creston above the Tyrsenians, and who were once neighbours of the race now called Dorian, dwelling then in the land which is now called Thessaliotis, and also by those that remain of the Pelasgians who settled at Plakia and Skylake in the region of the Hellespont, who before that had been settlers with the Athenians, and of the natives of the various other towns which are really Pelasgian, though they have lost the name,—if one must pronounce judging by these, the Pelasgians used to speak a Barbarian language. If therefore all the Pelasgian race was such as these, then the Attic race, being Pelasgian, at the same time when it changed and became Hellenic, unlearnt also its language. For the people of Creston do not speak the same language with any of those who dwell about them, nor yet do the people of Phakia, but they speak the same language one as the other: and by this it is proved that they still keep unchanged the form of language which they brought with them when they migrated to these places.

1.58 As for the Hellenic race, it has used ever the same language, as I clearly perceive, since it first took its rise; but since the time when it parted off feeble at first from the Pelasgian race, setting forth from a small beginning it has increased to that great number of races which we see, and chiefly because many Barbarian races have been added to it besides. Moreover it is true, as I think, of the Pelasgian race also, that so far as it remained Barbarian it never made any great increase. Thus, according to Herodotus, the Dorians did not name themselves after Dorus until they had reached Peloponnesus. Herodotus does not explain the contradictions of the myth; for example, how Doris, located outside the Peloponnesus, acquired its name. However, his goal, as he relates in the beginning of the first book, is only to report what he had heard from his sources without judgement. In the myth, the Achaeans displaced from the Peloponnesus gathered at Athens under a leader Ion and became identified as "Ionians".

Herodotus' list of Dorian states is as follows. From northeastern Greece were Phthia, Histiaea and Macedon. In central Greece were Doris (the former Dryopia) and in the south Peloponnesus, specifically the states of Lacedaemon, Corinth, Sicyon, Epidaurus and Troezen. Hermione was not Dorian but had joined the Dorians. Overseas were the islands of Rhodes, Cos, Nisyrus and the Anatolian cities of Cnidus, Halicarnassus, Phaselis and Calydna. Dorians also colonised Crete including founding of such towns as Lato, Dreros and Olous. The Cynurians were originally Ionians but had become Dorian under the influence of their Argive masters.

Thucydides
Thucydides professes little of Greece before the Trojan War except to say that it was full of barbarians and that there was no distinction between barbarians and Greeks. The Hellenes came from Phthiotis. The whole country indulged in and suffered from piracy and was not settled. After the Trojan War, "Hellas was still engaged in removing and settling."

Some 60 years after the Trojan War the Boeotians were driven out of Arne by the Thessalians into Boeotia and 20 years later "the Dorians and the Heraclids became masters of the Peloponnese." So the lines were drawn between the Dorians and the Aeolians (here Boeotians) with the Ionians (former Peloponnesians).

Other than these few brief observations Thucydides names but few Dorians. He does make it clear that some Dorian states aligned or were forced to align with the Athenians while some Ionians went with the Lacedaemonians and that the motives for alignment were not always ethnic but were diverse. Among the Dorians was Lacedaemon, Corcyra, Corinth and Epidamnus, Leucadia, Ambracia, Potidaea, Rhodes, Cythera, Argos, Syracuse, Gela, Acragas (later Agrigentum), Acrae, Casmenae.

He does explain with considerable dismay what happened to incite ethnic war after the unity between the Greek states during the Battle of Thermopylae. The Congress of Corinth, formed prior to it, "split into two sections." Athens headed one and Lacedaemon the other: "For a short time the league held together, till the Lacedaemonians and Athenians quarreled, and made war upon each other with their allies, a duel into which all the Hellenes sooner or later were drawn." He adds: "the real cause I consider to be ... the growth of the power of Athens and the alarm which this inspired in Lacedaemon...."

Plato
In the Platonic work Laws is mentioned that the Achaeans who fought in the Trojan War, on their return from Troy were driven out from their homes and cities by the young residents, so they migrated under a leader named Dorieus and hence they were renamed "Dorians". "Now during this period of ten years, while the siege lasted, the affairs of each of the besiegers at home suffered much owing to the seditious conduct of the young men. For when the soldiers returned to their own cities and homes, these young people did not receive them fittingly and justly, but in such a way that there ensued a vast number of cases of death, slaughter, and exile. So they, being again driven out, migrated by sea; and because Dorieus was the man who then banded together the exiles, they got the new name of 'Dorians', instead of 'Achaeans'. But as to all the events that follow this, you Lacedaemonians relate them all fully in your traditions."

Pausanias
The Description of Greece by Pausanias relates that the Achaeans were driven from their lands by Dorians coming from Oeta, a mountainous region bordering on Thessaly. They were led by Hyllus, a son of Heracles, but were defeated by the Achaeans. Under other leadership they managed to be victorious over the Achaeans and remain in the Peloponnesus, a mythic theme called "the return of the Heracleidae." They had built ships at Naupactus in which to cross the Gulf of Corinth. This invasion is viewed by the tradition of Pausanias as a return of the Dorians to the Peloponnesus, apparently meaning a return of families ruling in Aetolia and northern Greece to a land in which they had once had a share. The return is described in detail: there were "disturbances" throughout the Peloponnesus except in Arcadia, and new Dorian settlers. Pausanias goes on to describe the conquest and resettlement of Laconia, Messenia, Argos and elsewhere, and the emigration from there to Crete and the coast of Asia Minor.

Diodorus Siculus
Diodorus is a rich source of traditional information concerning the mythology and history of the Dorians, especially the Library of History. He does not make any such distinction but the fantastic nature of the earliest material marks it as mythical or legendary. The myths do attempt to justify some Dorian operations, suggesting that they were in part political.

Diodorus quoting from an earlier historian Hecataeus of Abdera details that during the Exodus many Israelites went into the islands of Greece and other places. All the foreigners were forthwith expelled, and the most valiant and noble among them, under some notable leaders, were brought to Greece and other places, as some relate; the most famous of their leaders were Danaus and Cadmus. But the majority of the people descended into a country not far from Egypt, which is now called Judaea and at that time was altogether uninhabited. Heracles was a Perseid, a member of the ruling family of Greece. His mother Alcmene had both Perseids and Pelopids in her ancestry. A princess of the realm, she received Zeus thinking he was Amphitryon. Zeus intended his son to rule Greece but according to the rules of succession Eurystheus, born slightly earlier, preempted the right. Attempts to kill Heracles as a child failed. On adulthood he was forced into the service of Eurystheus, who commanded him to perform 12 labors.

Heracles became a warrior without a home, wandering from place to place assisting the local rulers with various problems. He took a retinue of Arcadians with him acquiring also over time a family of grown sons, the Heraclidae. He continued this mode of life even after completing the 12 labors. The legend has it that he became involved with Achaean Sparta when the family of king Tyndareus was unseated and driven into exile by Hippocoön and his family, who in the process happened to kill the son of a friend of Heracles. The latter and his retinue assaulted Sparta, taking it back from Hippocoön. He recalled Tyndareus, set him up as a guardian regent, and instructed him to turn the kingdom over to any descendants of his that should claim it. Heracles went on with the way of life to which he had become accustomed, which was by today's standards that of a mercenary, as he was being paid for his assistance. Subsequently, he founded a colony in Aetolia, then in Trachis.

After displacing the Dryopes, he went to the assistance of the Dorians, who lived in a land called Hestiaeotis under king Aegimius and were campaigning against the numerically superior Lapithae. The Dorians promised him $1/3$ of Doris (which they did not yet possess). He asked Aegimius to keep his share of the land "in trust" until it should be claimed by a descendant. He went on to further adventures but was poisoned by his jealous wife, Deianeira. He immolated himself in full armor dressed for combat and "passed from among men into the company of the gods."

Strabo
Strabo, who depends on the books available to him, goes on to elaborate: "Of these peoples, according to Staphylus, the Dorians occupy the part toward the east, the Cydonians the western part, the Eteo-Cretans the southern; and to these last belongs the town Praisos, where is the temple of the Dictaean Zeus; whereas the other peoples, since they were more powerful, dwelt in the plains. Now it is reasonable to suppose that the Eteo-Cretans and the Cydonians were autochthonous, and that the others were foreigners ..." Beside this sole reference to Dorians in Crete, the mention of the Iliad of the Heraclid Tlepolemus, a warrior on the side of Achaeans and colonist of three important Dorian cities in Rhodes has been also regarded as a later interpolation.

title: Dorians


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Declaration of the Rights of Man and of the Citizen

The Declaration of the Rights of Man and of the Citizen (Déclaration des droits de l'Homme et du citoyen de 1789), set by France's National Constituent Assembly in 1789, is a human civil rights document from the French Revolution. Inspired by Enlightenment philosophers, the Declaration was a core statement of the values of the French Revolution and had a significant impact on the development of popular conceptions of individual liberty and democracy in Europe and worldwide.

The Declaration was initially drafted by Marquis de Lafayette, with assistance from Thomas Jefferson, but the majority of the final draft came from Abbé Sieyès. Influenced by the doctrine of natural right, human rights are held to be universal: valid at all times and in every place. It became the basis for a nation of free individuals protected equally by the law. It is included at the beginning of the constitutions of both the Fourth French Republic (1946) and Fifth Republic (1958), and is considered valid as constitutional law.

History
The content of the document emerged largely from the ideals of the Enlightenment. Lafayette prepared the principal drafts in consultation with his close friend Thomas Jefferson. In August 1789, Abbé Emmanuel Joseph Sieyès and Honoré Mirabeau played a central role in conceptualizing and drafting the final Declaration of the Rights of Man and of the Citizen.

The last article of the Declaration of the Rights of Man and the Citizen was adopted on the 26 of August 1789 by the National Constituent Assembly, during the period of the French Revolution, as the first step toward writing a constitution for France. Inspired by the Enlightenment, the original version of the Declaration was discussed by the representatives based on a 24-article draft proposed by, led by Jérôme Champion de Cicé. The draft was later modified during the debates. A second and lengthier declaration, known as the Declaration of the Rights of Man and Citizen of 1793, was written in 1793 but never formally adopted.

Background

The concepts in the Declaration come from the philosophical and political duties of the Enlightenment, such as individualism, the social contract as theorized by the Genevan philosopher Rousseau, and the separation of powers espoused by the Baron de Montesquieu. As can be seen in the texts, the French declaration was heavily influenced by the political philosophy of the Enlightenment and principles of human rights, as was the U.S. Declaration of Independence, which preceded it (4 July 1776).

These principles were shared widely throughout European society, rather than being confined to a small elite as in the past. This took different forms, such as 'English coffeehouse culture', and extended to areas colonised by Europeans, particularly British North America. Contacts between diverse groups in Edinburgh, Geneva, Boston, Amsterdam, Paris, London, or Vienna were much greater than often appreciated.

Transnational elites who shared ideas and styles were not new; what changed was their extent and the numbers involved. Under Louis XIV, Versailles was the centre of French culture, fashion and political power. Improvements in education and literacy over the course of the 18th century meant larger audiences for newspapers and journals, with Masonic lodges, coffee houses and reading clubs providing areas where people could debate and discuss ideas. The emergence of this "public sphere" led to Paris replacing Versailles as the cultural and intellectual centre, leaving the Court isolated and less able to influence opinion.

Assisted by Thomas Jefferson, then American ambassador to France, Lafayette prepared a draft which echoed some of the provisions of the US declaration. However, there was no consensus on the role of the Crown, and until this question was settled, it was impossible to create political institutions. When presented to the legislative committee on 11 July, it was rejected by pragmatists such as Jean Joseph Mounier, President of the Assembly, who feared creating expectations that could not be satisfied.

Conservatives like Gérard de Lally-Tollendal wanted a bicameral system, with an upper house appointed by the king, who would have the right of veto. On 10 September, the majority led by Sieyès and Talleyrand rejected this in favour of a single assembly, while Louis XVI retained only a "suspensive veto"; this meant he could delay the implementation of a law, but not block it. With these questions settled, a new committee was convened to agree on a constitution; the most controversial remaining issue was citizenship, itself linked to the debate on the balance between individual rights and obligations. Ultimately, the 1791 Constitution distinguished between 'active citizens' who held political rights, defined as French males over the age of 25, who paid direct taxes equal to three days' labour, and 'passive citizens', who were restricted to 'civil rights'. As a result, it was never fully accepted by radicals in the Jacobin club.

After editing by Mirabeau, it was published on 26 August as a statement of principle. The final draft contained provisions then considered radical in any European society, let alone France in 1789. French historian Georges Lefebvre argues that combined with the elimination of privilege and feudalism, it "highlighted equality in a way the (American Declaration of Independence) did not". More importantly, the two differed in intent; Jefferson saw the US Constitution and Bill of Rights as fixing the political system at a specific point in time, claiming they 'contained no original thought...but expressed the American mind' at that stage. The 1791 French Constitution was viewed as a starting point, the Declaration providing an aspirational vision, a key difference between the two Revolutions. Attached as a preamble to the French Constitution of 1791, and that of the 1870 to 1940 French Third Republic, it was incorporated into the current Constitution of France in 1958.

Summary of principles
The Declaration defined a single set of individual and collective rights for all men. Influenced by the doctrine of natural rights, these rights are held to be universal and valid in all times and places. For example, "Men are born and remain free and equal in rights. Social distinctions may be founded only upon the general good." They have certain natural rights to property, to liberty, and to life. According to this theory, the role of government is to recognize and secure these rights. Furthermore, the government should be carried on by elected representatives.

When it was written, the rights contained in the declaration were only awarded to men. Furthermore, the declaration was a statement of vision rather than reality. The declaration was not deeply rooted in either the practice of the West or even France at the time. The declaration emerged in the late 18th century out of war and revolution. It encountered opposition, as democracy and individual rights were frequently regarded as synonymous with anarchy and subversion. This declaration embodies ideals and aspirations towards which France pledged to struggle in the future.

Substance
The Declaration is introduced by a preamble describing the fundamental characteristics of the rights, which are qualified as "natural, unalienable and sacred" and "simple and incontestable principles" on which citizens could base their demands. In the second article, "the natural and imprescriptible rights of man" are defined as "liberty, property, security and resistance to oppression". It called for the destruction of aristocratic privileges by proclaiming an end to feudalism and to exemptions from taxation, freedom, and equal rights for all "Men" and access to public office based on talent. The monarchy was restricted, and all citizens had the right to participate in the legislative process. Freedom of speech and press were declared, and arbitrary arrests outlawed.

The Declaration also asserted the principles of popular sovereignty, in contrast to the divine right of kings that characterized the French monarchy, and social equality among citizens, "All the citizens, being equal in the eyes of the law, are equally admissible to all public dignities, places, and employments, according to their capacity and without distinction other than that of their virtues and of their talents," eliminating the special rights of the nobility and clergy.

Articles
Article I – Men are born and remain free and equal in rights. Social distinctions may be founded only upon the general good.

Article II – The goal of any political association is the conservation of the natural and imprescriptible rights of man. These rights are liberty, property, safety and resistance against oppression.

Article III – The principle of any sovereignty resides essentially in the Nation. No body, no individual may exercise any authority which does not proceed directly from the nation.

Article IV – Liberty consists of doing anything which does not harm others: thus, the exercise of the natural rights of each man has only those borders which assure other members of the society the fruition of these same rights. These borders can be determined only by the law.

Article V – The law has the right to forbid only actions harmful to society. Anything which is not forbidden by the law cannot be impeded, and no one can be constrained to do what it does not order.

Article VI – The law is the expression of the general will. All the citizens have the right of contributing personally or through their representatives to its formation. It must be the same for all, either that it protects, or that it punishes. All the citizens, being equal in its eyes, are equally admissible to all public dignities, places, and employments, according to their capacity and without distinction other than that of their virtues and of their talents.

Article VII – No man can be accused, arrested nor detained but in the cases determined by the law, and according to the forms which it has prescribed. Those who solicit, dispatch, carry out or cause to be carried out arbitrary orders, must be punished; but any citizen called or seized under the terms of the law must obey at once; he renders himself culpable by resistance.

Article VIII – The law should establish only penalties that are strictly and evidently necessary, and no one can be punished but under a law established and promulgated before the offense and legally applied.

Article IX – Any man being presumed innocent until he is declared culpable if it is judged indispensable to arrest him, any rigor which would not be necessary for the securing of his person must be severely reprimanded by the law.

Article X – No one may be disquieted for his opinions, even religious ones, provided that their manifestation does not trouble the public order established by the law.

Article XI – The free communication of thoughts and of opinions is one of the most precious rights of man: any citizen thus may speak, write, print freely, except to respond to the abuse of this liberty, in the cases determined by the law.

Article XII – The guarantee of the rights of man and of the citizen necessitates a public force: this force is thus instituted for the advantage of all and not for the particular utility of those in whom it is trusted.

Article XIII – For the maintenance of the public force and for the expenditures of administration, a common contribution is indispensable; it must be equally distributed to all the citizens, according to their ability to pay.

Article XIV – Each citizen has the right to ascertain, by himself or through his representatives, the need for a public tax, to consent to it freely, to know the uses to which it is put, and of determining the proportion, basis, collection, and duration.

Article XV – The society has the right of requesting an account from any public agent of its administration.

Article XVI – Any society in which the guarantee of rights is not assured, nor the separation of powers determined, has no Constitution.

Article XVII – Property being an inviolable and sacred right, no one can be deprived of private usage, if it is not when the public necessity, legally noted, evidently requires it, and under the condition of a just and prior indemnity.

Active and passive citizenship
While the French Revolution provided rights to a larger portion of the population, there remained a distinction between those who obtained the political rights in the Declaration of the Rights of Man and of the Citizen and those who did not. Those who were deemed to hold these political rights were called active citizens. Active citizenship was granted to men who were French, at least 25 years old, paid taxes equal to three days work, and could not be defined as servants. This meant that at the time of the Declaration, only male property owners held these rights. The deputies in the National Assembly believed that only those who held tangible interests in the nation could make informed political decisions. This distinction directly affects articles 6, 12, 14, and 15 of the Declaration of the Rights of Man and of the Citizen, as each of these rights is related to the right to vote and to participate actively in the government. With the decree of 29 October 1789, the term active citizen became embedded in French politics.

The concept of passive citizens was created to encompass those populations excluded from political rights in the Declaration of the Rights of Man and of the Citizen. Because of the requirements set down for active citizens, the vote was granted to approximately 4.3 million Frenchmen out of a population of around 29 million. These omitted groups included women, the poor, enslaved people, children, and foreigners. As the General Assembly voted upon these measures, they limited the rights of certain groups of citizens while implementing the democratic process of the new French Republic (1792–1804). This legislation, passed in 1789, was amended by the creators of the Constitution of the Year III to eliminate the label of an active citizen. The power to vote was then, however, to be granted solely to substantial property owners.

Tensions arose between active and passive citizens throughout the Revolution. This happened when passive citizens started to call for more rights or openly refused to listen to the ideals set forth by active citizens.

Women, in particular, were strong passive citizens who played a significant role in the Revolution. Olympe de Gouges penned her Declaration of the Rights of Woman and of the Female Citizen in 1791 and drew attention to the need for gender equality. By supporting the ideals of the French Revolution and wishing to expand them to women, she represented herself as a revolutionary citizen. Madame Roland also established herself as an influential figure throughout the Revolution. She saw women of the French Revolution as holding three roles; "inciting revolutionary action, formulating policy, and informing others of revolutionary events." By working with men, as opposed to working apart from men, she may have been able to further the fight for revolutionary women. As players in the French Revolution, women occupied a significant role in the civic sphere by forming social movements and participating in popular clubs, allowing them societal influence, despite their lack of direct political power.

Women's rights
The Declaration recognized many rights as belonging to citizens (who could only be male). This was despite the fact that after The March on Versailles on 5 October 1789, women presented the Women's Petition to the National Assembly in which they proposed a decree giving women equal rights. In 1790, Nicolas de Condorcet and Etta Palm d'Aelders unsuccessfully called on the National Assembly to extend civil and political rights to women. Condorcet declared that "he who votes against the right of another, whatever the religion, color, or sex of that other, has henceforth abjured his own". The French Revolution did not lead to a recognition of women's rights and this prompted Olympe de Gouges to publish the Declaration of the Rights of Woman and of the Female Citizen in September 1791.

The Declaration of the Rights of Woman and of the Female Citizen is modeled on the Declaration of the Rights of Man and of the Citizen and is ironic in the formulation and exposes the failure of the French Revolution, which had been devoted to equality. It states that:

"This revolution will only take effect when all women become fully aware of their deplorable condition, and of the rights, they have lost in society."

The Declaration of the Rights of Woman and of the Female Citizen follows the seventeen articles of the Declaration of the Rights of Man and of the Citizen point for point. Camille Naish has described it as "almost a parody... of the original document". The first article of the Declaration of the Rights of Man and of the Citizen proclaims that "Men are born and remain free and equal in rights. Social distinctions may be based only on common utility." The first article of the Declaration of the Rights of Woman and the Female Citizen replied: "Woman is born free and remains equal to man in rights. Social distinctions may only be based on common utility".

De Gouges also draws attention to the fact that under French law, women were fully punishable yet denied equal rights, declaring, "Women have the right to mount the scaffold, they must also have the right to mount the speaker's rostrum".

Slavery
The declaration did not revoke the institution of slavery, as lobbied for by Jacques-Pierre Brissot's Les Amis des Noirs and against by the group of colonial planters called the Club Massiac, because they met at the Hôtel Massiac. Despite the lack of explicit mention of slavery in the Declaration, slave uprisings in Saint-Domingue in the Haitian Revolution were inspired by it, as discussed in C. L. R. James's history of the Haitian Revolution, The Black Jacobins. In Louisiana, the organizers of the Pointe Coupée Slave Conspiracy of 1795 also drew information from the declaration.

Deplorable conditions for the thousands of enslaved people in Saint-Domingue, the most profitable slave colony in the world, led to the uprisings known as the first successful slave revolt in the New World. Free persons of color were part of the first wave of revolt, but later formerly enslaved people took control. In 1794, the convention was dominated by the Jacobins and abolished slavery, including in the colonies of Saint-Domingue and Guadeloupe. However, Napoleon reinstated it in 1802 and attempted to regain control of Saint-Domingue by sending in thousands of troops. After suffering the losses of two-thirds of the men, many to yellow fever, the French withdrew from Saint-Domingue in 1803. Napoleon gave up on North America and agreed to the Louisiana Purchase by the United States. In 1804, the leaders of Saint-Domingue declared it an independent state, the Republic of Haiti, the second republic of the New World. Napoleon abolished the slave trade in 1815. Slavery in France was finally abolished in 1848.

Homosexuality
The vast amount of personal freedom given to citizens by the document created a situation where homosexuality was decriminalized by the French Penal Code of 1791, which covered felonies; the law simply failed to mention sodomy as a crime, and thus no one could be prosecuted for it. The 1791 Code of Municipal Police did provide misdemeanor penalties for "gross public indecency," which the police could use to punish anyone having sex in public places or otherwise violating social norms. This approach to punishing homosexual conduct was reiterated in the French Penal Code of 1810.

Other early declarations of rights

 * The decreta of León (Kingdom of León (Modern Spain) 1188)
 * Magna Carta (England, 1215)
 * Kouroukan Fouga (Mali Empire, c. 1236)
 * Statute of Kalisz (Poland, 1264)
 * Henrician Articles and Pacta conventa (Poland, 1573)
 * Petition of Right (England, 1628)
 * Bill of Rights (England, 1689)
 * Claim of Right (Scotland, 1689)
 * Virginia Declaration of Rights (United States, 1776)
 * Pennsylvania Declaration of Rights (United States, 1776)
 * Bill of Rights (United States, 1789)
 * Declaration of the Rights of Man and Citizen of Franchimont (modern-day Belgium, 16 September 1789)
 * "Belgian" Declaration of the Rights of Man and Citizen (exiled Belgian and Liégeois revolutionaries in Paris, 23 April 1792)
 * (Poland, 7 May 1794)
 * "Batavian" Declaration of the Rights of Man and Citizen (Batavian Republic, The Hague, 31 January 1795)


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Dennis Ritchie

Dennis MacAlistair Ritchie (September 9, 1941 – c. October 12, 2011) was an American computer scientist. He created the C programming language and, with long-time colleague Ken Thompson, the Unix operating system and B language. Ritchie and Thompson were awarded the Turing Award from the Association for Computing Machinery (ACM) in 1983, the IEEE Richard W. Hamming Medal from the Institute of Electrical and Electronics Engineers (IEEE) in 1990, and the National Medal of Technology from President Bill Clinton in 1999.

Ritchie was the head of Lucent Technologies System Software Research Department when he retired in 2007.

Early life and education
Dennis Ritchie was born in Bronxville, New York. His father was Alistair E. Ritchie, a longtime Bell Labs scientist and co-author of The Design of Switching Circuits on switching circuit theory. As a child, Dennis moved with his family to Summit, New Jersey, where he graduated from Summit High School. He graduated from Harvard University with degrees in physics and applied mathematics in 1963.

Career
In 1967, Ritchie began working at the Bell Labs Computing Science Research Center. In 1968, he defended his PhD thesis on "Computational Complexity and Program Structure" at Harvard under the supervision of Patrick C. Fischer. However, Ritchie never officially received his PhD degree as he did not submit a bound copy of his dissertation to the Harvard library, a requirement for the degree. In 2020, the Computer History Museum worked with Ritchie's family and Fischer's family and found a copy of the lost dissertation.

During the 1960s, Ritchie and Ken Thompson worked on the Multics operating system at Bell Labs. Thompson then found an old PDP-7 machine and developed his own application programs and operating system from scratch, aided by Ritchie and others. In 1970, Brian Kernighan suggested the name "Unix", a pun on the name "Multics". To supplement assembly language with a system-level programming language, Thompson created B. Later, B was replaced by C, created by Ritchie, who continued to contribute to the development of Unix and C for many years.

During the 1970s, Ritchie collaborated with James Reeds and Robert Morris on a ciphertext-only attack on the M-209 US cipher machine that could solve messages of at least 2000–2500 letters. Ritchie relates that, after discussions with the National Security Agency, the authors decided not to publish it, as they were told that the principle applied to machines still in use by foreign governments.

Ritchie was also involved with the development of the operating systems Plan 9 and Inferno, and the programming language Limbo.

As part of an AT&T restructuring in the mid-1990s, Ritchie was transferred to Lucent Technologies, where he retired in 2007 as head of System Software Research Department.

C and Unix
Ritchie created the C programming language and was one of the developers of the Unix operating system. With Brian Kernighan, he co-wrote the book The C Programming Language, which is often referred to as K&R after their initials. Ritchie worked together with Ken Thompson, who is credited with writing the original version of Unix; one of Ritchie's contributions to Unix was its porting to different machines and platforms. They were so influential on Research Unix that Doug McIlroy later wrote, "The names of Ritchie and Thompson may safely be assumed to be attached to almost everything not otherwise attributed."

Nowadays, the C language is widely used in application, operating system, and embedded system development, and its influence is seen in most modern programming languages. C is a low-level language with constructs closely translating to the hardware's instruction set. However, it is not tied to any given hardware, making it easy to write programs on any machine that supports C. Moreover, C is a high-level programming language with constructs mapping to data structures in application software.

C influenced several other languages and derivatives, such as C++, Objective-C used by Apple, C# used by Microsoft, and Java used in corporate environments extensively and by Android. Ritchie and Thompson used C to write Unix, which has been influential in establishing many computing concepts and principles that are adopted widely.

In an interview from 1999, Ritchie clarified that he saw Linux and Berkeley Software Distribution (BSD) operating systems as a continuation of the basis of the Unix operating system, and as derivatives of Unix:

"I think the Linux phenomenon is quite delightful, because it draws so strongly on the basis that Unix provided. Linux seems to be among the healthiest of the direct Unix derivatives, though there are also the various BSD systems as well as the more official offerings from the workstation and mainframe manufacturers."

In the same interview, he stated that he viewed Unix and Linux as "the continuation of ideas that were started by Ken and me and many others, many years ago."

Awards
In 1983, Ritchie and Thompson received the Turing Award "for their development of generic operating systems theory and specifically for the implementation of the UNIX operating system". Ritchie's Turing Award lecture was titled "Reflections on Software Research". In 1990, both Ritchie and Thompson received the IEEE Richard W. Hamming Medal from the Institute of Electrical and Electronics Engineers (IEEE), "for the origination of the UNIX operating system and the C programming language".

In 1997, both Ritchie and Thompson were made Fellows of the Computer History Museum, "for co-creation of the UNIX operating system, and for development of the C programming language."

On April 21, 1999, Thompson and Ritchie jointly received the National Medal of Technology of 1998 from President Bill Clinton for co-inventing the UNIX operating system and the C programming language which, according to the citation for the medal, "led to enormous advances in computer hardware, software, and networking systems and stimulated growth of an entire industry, thereby enhancing American leadership in the Information Age".

In 2005, the Industrial Research Institute awarded Ritchie its Achievement Award in recognition of his contribution to science and technology, and to society generally, with his development of the Unix operating system.

In 2011, Ritchie, along with Thompson, was awarded the Japan Prize for Information and Communications for his work in the development of the Unix operating system.

Death

Ritchie was found dead on October 12, 2011, at the age of 70 at his home in Berkeley Heights, New Jersey, where he lived alone. First news of his death came from his former colleague, Rob Pike. He had been in frail health for several years following treatment for prostate cancer and heart disease. News of Ritchie's death was largely overshadowed by the media coverage of the death of Apple co-founder Steve Jobs, which occurred the week before.

Legacy
Following Ritchie's death, computer historian Paul E. Ceruzzi stated:

"Ritchie was under the radar. His name was not a household name at all, but... if you had a microscope and could look in a computer, you'd see his work everywhere inside."

In an interview shortly after Ritchie's death, long-time colleague Brian Kernighan said Ritchie never expected C to be so significant. Kernighan told The New York Times "The tools that Dennis built—and their direct descendants—run pretty much everything today." Kernighan reminded readers of how important a role C and Unix had played in the development of later high-profile projects, such as the iPhone. Other testimonials to his influence followed.

Reflecting upon his death, a commentator compared the relative importance of Steve Jobs and Ritchie, concluding that "[Ritchie's] work played a key role in spawning the technological revolution of the last forty years—including technology on which Apple went on to build its fortune." Another commentator said, "Ritchie, on the other hand, invented and co-invented two key software technologies which make up the DNA of effectively every single computer software product we use directly or even indirectly in the modern age. It sounds like a wild claim, but it really is true." Another said, "many in computer science and related fields knew of Ritchie's importance to the growth and development of, well, everything to do with computing,..."

The Fedora 16 Linux distribution, which was released about a month after he died, was dedicated to his memory. FreeBSD 9.0, released January 12, 2012, was also dedicated in his memory.

Asteroid 294727 Dennisritchie, discovered by astronomers Tom Glinos and David H. Levy in 2008, was named in his memory. The official was published by the Minor Planet Center on 7 February 2012 (Minor Planet Circulars (M.P.C.) 78272).

Notable works

 * B language
 * C language on which many succeeding languages and technologies are based.
 * Unix multiuser operating system. Several workalikes (commonly referred to as Unix-like systems) have been developed based on Unix's design. Some follow POSIX standards, again based on Unix.
 * Unix Programmer's Manual (1971)
 * The C Programming Language (sometimes referred to as K&R; 1978 with Brian Kernighan)

Publications and academic papers
Ritchie has been the author or contributor to about 50 academic papers, books and textbooks and which have had over 15,000 citations.

Here are some of his most cited works:

 * The C Programming Language, BW Kernighan, DM Ritchie, Prentice Hall, Englewood Cliffs, New Jersey (1978)
 * Programming languages, D Ritchie (1978)
 * The UNIX time-sharing system, DM Ritchie, K Thompson, Classic operating systems, 195-220 (2001)
 * Advanced Programming in the Unix Environment, WR Stevens, SA Rago, DM Ritchie, Addison-Wesley (1992, 2008)

title: Dennis Ritchie