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Sigma
Sigma (; uppercase Σ, lowercase σ, lowercase in word-final position ς; grc-gre, σίγμα) is the eighteenth letter of the Greek alphabet. In the system of Greek numerals, it has a value of 200. In general mathematics, uppercase Σ is used as an operator for summation. When used at the end of a letter-case word (one that does not use all caps), the final form (ς) is used. In ' (Odysseus), for example, the two lowercase sigmas (σ) in the center of the name are distinct from the word-final sigma (ς) at the end. The Latin letter S derives from sigma while the Cyrillic letter Es derives from a lunate form of this letter. History The shape (Σς) and alphabetic position of sigma is derived from the Phoenician letter ( ''shin''). Sigma's original name may have been ''san'', but due to the complicated early history of the Greek epichoric alphabets, ''san'' came to be identified as a separate letter in the Greek alphabet, represented as Ϻ. Herodotus reports that "san" wa ...
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Greek Alphabet
The Greek alphabet has been used to write the Greek language since the late 9th or early 8th century BCE. It is derived from the earlier Phoenician alphabet, and was the earliest known alphabetic script to have distinct letters for vowels as well as consonants. In Archaic Greece, Archaic and early Classical Greece, Classical times, the Greek alphabet existed in Archaic Greek alphabets, many local variants, but, by the end of the 4th century BCE, the Euclidean alphabet, with 24 letters, ordered from alpha to omega, had become standard and it is this version that is still used for Greek writing today. The letter case, uppercase and lowercase forms of the 24 letters are: : , , , , , , , , , , , , , , , , , /ς, , , , , , . The Greek alphabet is the ancestor of the Latin script, Latin and Cyrillic scripts. Like Latin and Cyrillic, Greek originally had only a single form of each letter; it developed the letter case distinction between uppercase and lowercase in parallel with Latin ...
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Summation
In mathematics, summation is the addition of a sequence of any kind of numbers, called ''addends'' or ''summands''; the result is their ''sum'' or ''total''. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined. Summations of infinite sequences are called series. They involve the concept of limit, and are not considered in this article. The summation of an explicit sequence is denoted as a succession of additions. For example, summation of is denoted , and results in 9, that is, . Because addition is associative and commutative, there is no need of parentheses, and the result is the same irrespective of the order of the summands. Summation of a sequence of only one element results in this element itself. Summation of an empty sequence (a sequence with no elements), by convention, results in 0. Very often, the elements ...
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Greek Numerals
Greek numerals, also known as Ionic, Ionian, Milesian, or Alexandrian numerals, are a system of writing numbers using the letters of the Greek alphabet. In modern Greece, they are still used for ordinal numbers and in contexts similar to those in which Roman numerals are still used in the Western world. For ordinary cardinal numbers, however, modern Greece uses Arabic numerals. History The Minoan and Mycenaean civilization Mycenaean Greece (or the Mycenaean civilization) was the last phase of the Bronze Age in Ancient Greece, spanning the period from approximately 1750 to 1050 BC.. It represents the first advanced and distinctively Greek civilization in mainland ...s' Linear A and Linear B alphabets used a different system, called Aegean numerals, which included number-only symbols for powers of ten:  = 1,  = 10,  = 100,  = 1000, and  = 10000. Attic numerals comprised another system that came into use perhaps in th ...
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Es (Cyrillic)
Es (С с; italics: ) is a letter of the Cyrillic script. It commonly represents the voiceless alveolar fricative , like the pronunciation of in "sand". History The Cyrillic letter Es is derived from a variant of the Greek letter Sigma known as ''lunate sigma'' (Ϲ ϲ), in use in the Greek-speaking world in early medieval times. It has no connection to the Latin letter C (C c), which is a descendant of the Greek letter Gamma (Γ γ); however, many languages (for different reasons) apply the value of to the Latin letter C, especially before front vowels ''e'' and ''i'' (examples being English, French, Mexican Spanish); see hard and soft C. As its name suggests, Es is related to the Latin S. The name of Es in the Early Cyrillic alphabet was (''slovo''), meaning "word" or "speech". In the Cyrillic numeral system, Es had a value of 200. Form In the modern Latinized Cyrillic fonts in use today, the Cyrillic letter Es looks exactly like the Latin let ...
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Archaic Greek Alphabets
Many local variants of the Greek alphabet were employed in ancient Greece during the archaic and early classical periods, until around 400 BC, when they were replaced by the classical 24-letter alphabet that is the standard today. All forms of the Greek alphabet were originally based on the shared inventory of the 22 symbols of the Phoenician alphabet, with the exception of the letter Samekh, whose Greek counterpart Xi () was used only in a sub-group of Greek alphabets, and with the common addition of Upsilon () for the vowel . The local, so-called ''epichoric'', alphabets differed in many ways: in the use of the consonant symbols , and ; in the use of the innovative long vowel letters ( and ), in the absence or presence of Η in its original consonant function (); in the use or non-use of certain archaic letters ( = , = , = ); and in many details of the individual shapes of each letter. The system now familiar as the standard 24-letter Greek alphabet was originally ...
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San (letter)
San (Ϻ) was an archaic letter of the Greek alphabet. Its shape was similar to modern M or Mu, or to a modern Greek Sigma (Σ) turned sideways, and it was used as an alternative to Sigma to denote the sound . Unlike Sigma, whose position in the alphabet is between Rho and Tau, San appeared between Pi and Qoppa in alphabetic order. In addition to denoting this separate archaic character, the name San was also used as an alternative name to denote the standard letter Sigma. Historical use Sigma and san The existence of the two competing letters Sigma and San is traditionally believed to have been due to confusion during the adoption of the Greek alphabet from the Phoenician script, because Phoenician had more sibilant sounds than Greek had. According to one theory, the distribution of the sibilant letters in Greek is due to pair-wise confusion between the sounds and alphabet positions of the four Phoenician sibilant signs: Greek Sigma got its shape and alphabetic position fr ...
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