The Kharosthi script spelled Kharoshthi or Kharoṣṭhī, was an ancient Indian script used in Gandhara to write Gandhari Prakrit and Sanskrit. It was popular in Central Asia as well. An abugida, it was introduced at least by the middle of the 3rd century BCE during the 4th century BCE, remained in use until it died out in its homeland around the 3rd century CE, it was in use in Bactria, the Kushan Empire and along the Silk Road, where there is some evidence it may have survived until the 7th century in the remote way stations of Khotan and Niya. Kharosthi is encoded in the Unicode range U+10A00–U+10A5F, from version 4.1. Kharosthi is written right to left, but some inscriptions show the left to right direction, to become universal for the South Asian scripts; each syllable includes the short /a/ sound by default, with other vowels being indicated by diacritic marks. Recent epigraphic evidence highlighted by Professor Richard Salomon of the University of Washington has shown that the order of letters in the Kharosthi script follows what has become known as the Arapacana alphabet.
As preserved in Sanskrit documents, the alphabet runs: a ra pa ca na la da ba ḍa ṣa va ta ya ṣṭa ka sa ma ga stha ja śva dha śa kha kṣa sta jñā rtha bha cha sma hva tsa gha ṭha ṇa pha ska ysa śca ṭa ḍhaSome variations in both the number and order of syllables occur in extant texts. Kharosthi includes only one standalone vowel, used for initial vowels in words. Other initial vowels use the a character modified by diacritics. Using epigraphic evidence, Salomon has established that the vowel order is /a e i o u/, rather than the usual vowel order for Indic scripts /a i u e o/; that is the same as the Semitic vowel order. There is no differentiation between long and short vowels in Kharosthi. Both are marked using the same vowel markers; the alphabet was used in Gandharan Buddhism as a mnemonic for remembering a series of verses on the nature of phenomena. In Tantric Buddhism, the list was incorporated into ritual practices and became enshrined in mantras. There are two special modified forms of these consonants: Various additional marks are used to modify vowels and consonants: Nine Kharosthi punctuation marks have been identified: Kharosthi included a set of numerals that are reminiscent of Roman numerals.
The system is based on an additive and a multiplicative principle, but does not have the subtractive feature used in the Roman number system. The numerals, like the letters, are written from right to left. There is no zero and no separate signs for the digits 5–9. Numbers in Kharosthi use an additive system. For example, the number 1996 would be written as 1000 4 4 1 100 20 20 20 20 10 4 2; the Kharosthi script was deciphered by James Prinsep using the bilingual coins of the Indo-Greek Kingdom. This in turn led to the reading of the Edicts of Ashoka, some of which, from the northwest of South Asia, were written in the Kharosthi script. Scholars are not in agreement as to whether the Kharosthi script evolved or was the deliberate work of a single inventor. An analysis of the script forms shows a clear dependency on the Aramaic alphabet but with extensive modifications to support the sounds found in Indic languages. One model is that the Aramaic script arrived with the Achaemenid Empire's conquest of the Indus River in 500 BCE and evolved over the next 200+ years, reaching its final form by the 3rd century BCE where it appears in some of the Edicts of Ashoka found in northwestern part of South Asia.
However, no intermediate forms have yet been found to confirm this evolutionary model, rock and coin inscriptions from the 3rd century BCE onward show a unified and standard form. An inscription in Aramaic dating back to the 4th century BCE was found in Sirkap, testifying to the presence of the Aramaic script in northwestern India at that period. According to Sir John Marshall, this seems to confirm that Kharoshthi was developed from Aramaic; the study of the Kharosthi script was invigorated by the discovery of the Gandhāran Buddhist texts, a set of birch bark manuscripts written in Kharosthi, discovered near the Afghan city of Hadda just west of the Khyber Pass in Pakistan. The manuscripts were donated to the British Library in 1994; the entire set of manuscripts are dated to the 1st century CE, making them the oldest Buddhist manuscripts yet discovered. Kharosthi was added to the Unicode Standard in March, 2005 with the release of version 4.1. The Unicode block for Kharosthi is U+10A00–U+10A5F: Brahmi History of Afghanistan History of Pakistan Pre-Islamic scripts in Afghanistan Kaschgar und die Kharoṣṭhī Dani, Ahmad Hassan.
Kharoshthi Primer, Lahore Museum Publication Series - 16, Lahore, 1979 Falk, Harry. Schrift im alten Indien: Ein Forschungsbericht mit Anmerkungen, Gunter Narr Verlag, 1993 Fussman's, Gérard. Les premiers systèmes d'écriture en Inde, in Annuaire du Collège de France 1988-1989 Hinüber, Oscar von. Der Beginn der Schrift und frühe Schriftlichkeit in Indien, Franz Steiner Verlag, 1990 Nasim Khan, M.. Ashokan Inscriptions: A Palaeographical Study. Atthariyyat, Vol. I, pp. 131–150. Peshawar Nasim Khan, M.. Two Dated Kharoshthi Inscriptions from Gandhara. Journal of Asian Civilizations, Vol. XXII, No.1, July 1999: 99-103. Nasim Khan, M.. An Inscribed Relic-Casket from Dir; the Journal of Humanities and Social Sciences, Vol. V, No. 1, March 1997: 21-33. Peshawar Nasim Khan, M.. Kharoshthi Inscription from Swabi - Gandhara; the Journal of Humanities and Soc
The Mayan numeral system was the system to represent numbers and calendar dates in the Maya civilization. It was a vigesimal positional numeral system; the numerals are made up of three symbols. For example, thirteen is written as three dots in a horizontal row above two horizontal bars. With these three symbols each of the twenty vigesimal digits could be written. Numbers after 19 were written vertically in powers of twenty; the Mayan used powers of twenty, just as the Hindu–Arabic numeral system uses powers of tens. For example, thirty-three would be written as one dot, above three dots atop two bars; the first dot represents "one twenty" or "1×20", added to three dots and two bars, or thirteen. Therefore, + 13 = 33. Upon reaching 202 or 400, another row is started; the number 429 would be written as one dot above one dot above four dots and a bar, or + + 9 = 429. Other than the bar and dot notation, Maya numerals were sometimes illustrated by face type glyphs or pictures; the face glyph for a number represents the deity associated with the number.
These face number glyphs were used, are seen on some of the most elaborate monumental carving. Adding and subtracting numbers below 20 using Maya numerals is simple. Addition is performed by combining the numeric symbols at each level: If five or more dots result from the combination, five dots are removed and replaced by a bar. If four or more bars result, four bars are removed and a dot is added to the next higher row. With subtraction, remove the elements of the subtrahend symbol from the minuend symbol: If there are not enough dots in a minuend position, a bar is replaced by five dots. If there are not enough bars, a dot is removed from the next higher minuend symbol in the column and four bars are added to the minuend symbol, being worked on; the "Long Count" portion of the Maya calendar uses a variation on the vigesimal numbering. In the second position, only the digits up to 17 are used, the place value of the third position is not 20×20 = 400, as would otherwise be expected, but 18×20 = 360, so that one dot over two zeros signifies 360.
This is because 360 is the number of days in a year. Subsequent positions use all twenty digits and the place values continue as 18×20×20 = 7,200 and 18×20×20×20 = 144,000, etc; every known example of large numbers in the Maya system uses this'modified vigesimal' system, with the third position representing multiples of 18×20. It is reasonable to assume, but not proven by any evidence, that the normal system in use was a pure base-20 system. Several Mesoamerican cultures used similar numerals and base-twenty systems and the Mesoamerican Long Count calendar requiring the use of zero as a place-holder; the earliest long count date is from 36 BC. Since the eight earliest Long Count dates appear outside the Maya homeland, it is assumed that the use of zero and the Long Count calendar predated the Maya, was the invention of the Olmec. Indeed, many of the earliest Long Count dates were found within the Olmec heartland. However, the Olmec civilization had come to an end by the 4th century BC, several centuries before the earliest known Long Count dates—which suggests that zero was not an Olmec discovery.
Mayan numerals were added to the Unicode Standard in June, 2018 with the release of version 11.0. The Unicode block for Mayan Numerals is U+1D2E0–U+1D2FF: Maya Mathematics - online converter from decimal numeration to Maya numeral notation. Anthropomorphic Maya numbers - online story of number representations. BabelStone Mayan Numerals - free font for Unicode Mayan numeral characters
Tamil numerals, refers to the numeral system of the Tamil language used in Tamil Nadu and Singapore, as well as by the other Tamil-speaking populations around the world including Sri Lanka, Mauritius, Réunion, South Africa, other emigrant communities around the world. Old Tamil possesses a special numerical character for zero and it is read as andru, but yet Modern Tamil renounces the use of its native character and uses Arabic, 0. Modern Tamil words for zero include சுழியம் or பூச்சியம். Tamil has a numeric prefix for each number from 1 to 9, which can be added to the words for the powers of ten to form multiples of them. For instance, the word for fifty, ஐம்பது is a combination of ஐ and பத்து; the prefix for nine changes with respect to the succeeding base 10. தொ+ the unvoiced consonant of the succeeding base 10 forms the prefix for nine. For instance, 90 is தொ+ண், hence, தொண்ணூறு); these are void in the Tamil language except for some Hindu and Christian religious references, example'அட்ட இலட்சுமிகள்' in a Hindu context, or'ஏக பாலன்' in a Christian context.
However, it should be noted, that in religious contexts Tamil language is more preferred for its more poetic nature and low incidence of consonant clusters. Unlike other Indian writing systems, Tamil has distinct digits for 10, 100, 1000, it has distinct characters for other number-based aspects of day-to-day life. There are two numeral systems that can be used in the Tamil language: the Tamil system, as followsThe following are the traditional numbers of the Ancient Tamil Country, Tamizhakam. Proposals to encode Tamil fractions and symbols to Unicode were submitted; as of version 12.0, Tamil characters used for fractional values in traditional accounting practices were added to the Unicode Standard. You can transcribe any fraction, by affixing -இல் after the denominator followed by the numerator. For instance, 1/41 can be said as நாற்பத்து ஒன்றில் ஒன்று; the suffixing of the -இல் requires you to change the last consonant of the number to its இ form. For example, மூன்று+இல் becomes மூன்றில். Common fractions have names allocated to them, these names are used rather than the above method.
Other fractions include: ^ Aṇu was considered as the lowest fraction by ancient Tamils as size of smallest physical object. This term went to Sanskrit to refer directly to atoms. Decimal point is called புள்ளி in Tamil. For example, 1.1 would be read as ஒன்று புள்ளி ஒன்று. Percentage is known as விழுக்காடு in Tamil or சதவீதம்; these words are added after a number to form percentages. For instance, four percent is நான்கு சதவீதம் or நான்கு விழுக்காடு. Percentage symbol is recognised and used. Ordinal numbers are formed by adding the suffix -ஆம் after the number, except for'First'; as always, when blending two words into one, an unvoiced form of the consonant as the one that the second starts with, is placed in between to blend. This song is a list of each number with a concept its associated with; as the antique classical language of the Dravidian languages, Tamil numerals influenced and shaped the numerals of the others in the family. The following table compares the main Dravidian languages. Tamil through the Pallava script which itself through the Kawi script, Khmer script and other South-east Asian scripts has shaped the numeral grapheme of most South-east Asian languages.
Before the Government of India unveiled ₹ as the new rupee symbol, people in Tamil Nadu used the Tamil letter ௹ as the symbol. This symbol continues to be used as rupee symbol by Indian Tamils out of habit, it is used by Tamils in Sri Lanka ௳ is known as the Pillaiyar Suzhi. The Tamil numbers used symbols; the Sanskrit numerals are as follows: 1- ekam 2- dhwey 3- thrini 4- chathwari 5- pancha 6- shad 7- saptha 8- ashta 9- nava 10- dhasa Tamil script Tamil units of measurement
Geʽez known as Ethiopic, is a script used as an abugida for several languages of Eritrea and Ethiopia. It originated as an abjad and was first used to write Geʽez, now the liturgical language of the Eritrean Orthodox Tewahedo Church, the Ethiopian Orthodox Tewahedo Church, Beta Israel, the Jewish community in Ethiopia. In Amharic and Tigrinya, the script is called fidäl, meaning "script" or "alphabet"; the Geʽez script has been adapted to write other Semitic, languages Amharic in Ethiopia, Tigrinya in both Eritrea and Ethiopia. It is used for Sebatbeit, Meʼen, most other languages of Ethiopia. In Eritrea it is used for Tigre, it has traditionally been used for Blin, a Cushitic language. Tigre, spoken in western and northern Eritrea, is considered to resemble Geʽez more than do the other derivative languages; some other languages in the Horn of Africa, such as Oromo, used to be written using Geʽez, but have migrated to Latin-based orthographies. For the representation of sounds, this article uses a system, common among linguists who work on Ethiopian Semitic languages.
This differs somewhat from the conventions of the International Phonetic Alphabet. See the articles on the individual languages for information on the pronunciation; the earliest inscriptions of Semitic languages in Eritrea and Ethiopia date to the 9th century BC in Epigraphic South Arabian, an abjad shared with contemporary kingdoms in South Arabia. After the 7th and 6th centuries BC, variants of the script arose, evolving in the direction of the Geʽez abugida; this evolution can be seen most in evidence from inscriptions in Tigray region in northern Ethiopia and the former province of Akkele Guzay in Eritrea. By the first centuries AD, what is called "Old Ethiopic" or the "Old Geʽez alphabet" arose, an abjad written left-to-right with letters identical to the first-order forms of the modern vocalized alphabet. There were minor differences such as the letter "g" facing to the right, instead of to the left as in vocalized Geʽez, a shorter left leg of "l", as in ESA, instead of equally-long legs in vocalized Geʽez.
Vocalization of Geʽez occurred in the 4th century, though the first vocalized texts known are inscriptions by Ezana, vocalized letters predate him by some years, as an individual vocalized letter exists in a coin of his predecessor Wazeba. Linguist Roger Schneider has pointed out anomalies in the known inscriptions of Ezana that imply that he was consciously employing an archaic style during his reign, indicating that vocalization could have occurred much earlier; as a result, some believe that the vocalization may have been adopted to preserve the pronunciation of Geʽez texts due to the moribund or extinct status of Geʽez, that, by that time, the common language of the people were later Ethio-Semitic languages. At least one of Wazeba's coins from the late 3rd or early 4th century contains a vocalized letter, some 30 or so years before Ezana. Kobishchanov and others have suggested possible influence from the Brahmic family of alphabets in vocalization, as they are abugidas, Aksum was an important part of major trade routes involving India and the Greco-Roman world throughout the common era of antiquity.
According to the beliefs of the Eritrean Orthodox Tewahedo Church and Ethiopian Orthodox Tewahedo Church, the original consonantal form of the Geʽez fidel was divinely revealed to Henos "as an instrument for codifying the laws", the present system of vocalisation is attributed to a team of Aksumite scholars led by Frumentius, the same missionary said to have converted the king Ezana to Christianity in the 4th century AD. It has been argued that the vowel marking pattern of the script reflects a South Asian system, such as would have been known by Frumentius. A separate tradition, recorded by Aleqa Taye, holds that the Geʽez consonantal alphabet was first adapted by Zegdur, a legendary king of the Ag'azyan Sabaean dynasty held to have ruled in Ethiopia c. 1300 BC. Geʽez has 26 consonantal letters. Compared to the inventory of 29 consonants in the South Arabian alphabet, continuants are missing of ġ, ẓ, South Arabian s3, as well as z and ṯ, these last two absences reflecting the collapse of interdental with alveolar fricatives.
On the other hand, emphatic P̣ait ጰ, a Geʽez innovation, is a modification of Ṣädai ጸ, while Pesa ፐ is based on Tawe ተ. Thus, there are 24 correspondences of Geʽez and the South Arabian alphabet: Many of the letter names are cognate with those of Phoenician, may thus be assumed for Proto-Sinaitic. Two alphabets were used to write the Geʽez language, an abjad and an abugida; the abjad, used until c. 330 AD, had 26 consonantal letters: h, l, ḥ, m, ś, r, s, ḳ, b, t, ḫ, n, ʾ, k, w, ʿ, z, y, d, g, ṭ, p̣, ṣ, ṣ́, f, p Vowels were not indicated. Modern Geʽez is written from left to right; the Geʽez abugida developed under the influence of Christian scripture by adding obligatory vocalic diacritics to the consonantal letters. The diacritics for the vowels, u, i, a, e, ə, o, were fused with the consonants in a recognizable but irregular way, so that the system is laid out as a syllabary; the original form of the consonant was used when the vowel was the so-called inherent vowel. The resulting forms are shown below in their traditional order.
For some vowels, there is an eighth form for the diphthong -wa or -oa
Counting rods are small bars 3–14 cm long, that were used by mathematicians for calculation in ancient East Asia. They are placed either horizontally or vertically to represent any rational number; the written forms based on them are called rod numerals. They are a true positional numeral system with digits for 1–9 and a blank for 0, from the Warring states period to the 16th century. Chinese arithmeticians used counting rods well over two thousand years ago. In 1954 forty-odd counting rods of the Warring States period were found in Zuǒjiāgōngshān Chu Grave No.15 in Changsha, Hunan. In 1973 archeologists unearthed a number of wood scripts from a tomb in Hubei dating from the period of the Han dynasty. On one of the wooden scripts was written: "当利二月定算"; this is one of the earliest examples of using counting-rod numerals in writing. In 1976 a bundle of Western Han-era counting rods made of bones was unearthed from Qianyang County in Shaanxi; the use of counting rods must predate it. The Book of Han recorded: "they calculate with bamboo, diameter one fen, length six cun, arranged into a hexagonal bundle of two hundred seventy one pieces".
At first, calculating rods were round in cross-section, but by the time of the Sui dynasty mathematicians used triangular rods to represent positive numbers and rectangular rods for negative numbers. After the abacus flourished, counting rods were abandoned except in Japan, where rod numerals developed into a symbolic notation for algebra. Counting rods represent digits by the number of rods, the perpendicular rod represents five. To avoid confusion and horizontal forms are alternately used. Vertical rod numbers are used for the position for the units, ten thousands, etc. while horizontal rod numbers are used for the tens, hundred thousands etc. It is written in Sunzi Suanjing that "one is vertical, ten is horizontal". Red rods represent black rods represent negative numbers. Ancient Chinese understood negative numbers and zero, though they had no symbol for the latter; the Nine Chapters on the Mathematical Art, composed in the first century CE, stated " subtract same signed numbers, add different signed numbers, subtract a positive number from zero to make a negative number, subtract a negative number from zero to make a positive number".
A go stone was sometimes used to represent zero. This alternation of vertical and horizontal rod numeral form is important to understanding written transcription of rod numerals on manuscripts correctly. For instance, in Licheng suanjin, 81 was transcribed as, 108 was transcribed as. In the same manuscript, 405 was transcribed as, with a blank space in between for obvious reasons, could in no way be interpreted as "45". In other words, transcribed rod numerals may not be positional, but on the counting board, they are positional. is an exact image of the counting rod number 405 on a table top or floor. The value of a number depends on its physical position on the counting board. A 9 at the rightmost position on the board stands for 9. Moving the batch of rods representing 9 to the left one position gives 9 or 90. Shifting left again to the third position gives 9 or 900; each time one shifts a number one position to the left, it is multiplied by 10. Each time one shifts a number one position to the right, it is divided by 10.
This applies to multiple-digit numbers. Song dynasty mathematician Jia Xian used hand-written Chinese decimal orders 步十百千萬 as rod numeral place value, as evident from a facsimile from a page of Yongle Encyclopedia, he arranged 七萬一千八百二十四 as 七一八二四 萬千百十步He treated the Chinese order numbers as place value markers, 七一八二四 became place value decimal number. He wrote the rod numerals according to their place value: In Japan, mathematicians put counting rods on a counting board, a sheet of cloth with grids, used only vertical forms relying on the grids. An 18th-century Japanese mathematics book has a checker counting board diagram, with the order of magnitude symbols "千百十一分厘毛“. Examples: Rod numerals are a positional numeral system made from shapes of counting rods. Positive numbers are written as they are and the negative numbers are written with a slant bar at the last digit; the vertical bar in the horizontal forms 6–9 are drawn shorter to have the same character height. A circle is used for 0. Many historians think it was imported from Indian numerals by Gautama Siddha in 718, but some think it was created from the Chinese text space filler "□", others think that the Indians acquired it from China, because it resembles a Confucian philosophical symbol for nothing.
In the 13th century, Southern Song mathematicians changed digits for 4, 5, 9 to reduce strokes. The new horizontal forms transformed into Suzhou numerals. Japanese continued to use the traditional forms. Examples: In Japan, Seki Takakazu developed the rod num
The Brahmi numerals are a numeral system attested from the 3rd century BCE. They are the direct graphic ancestors of the modern Hindu -- Arabic numerals. However, they were conceptually distinct from these systems, as they were not used as a positional system with a zero. Rather, there were separate numerals for each of the tens. There were symbols for 100 and 1000 which were combined in ligatures with the units to signify 200, 300, 2000, 3000, etc; the source of the first three numerals seems clear: they are collections of 1, 2, 3 strokes, in Ashoka's era vertical I, II, III like Roman numerals, but soon becoming horizontal like the modern Chinese numerals. In the oldest inscriptions, 4 is a +, reminiscent of the X of neighboring Kharoṣṭhī, a representation of 4 lines or 4 directions. However, the other unit numerals appear to be arbitrary symbols in the oldest inscriptions, it is sometimes supposed that they may have come from collections of strokes, run together in cursive writing in a way similar to that attested in the development of Egyptian hieratic and demotic numerals, but this is not supported by any direct evidence.
The units for the tens are not related to each other or to the units, although 10, 20, 80, 90 might be based on a circle. The sometimes rather striking graphic similarity they have with the hieratic and demotic Egyptian numerals, while suggestive, is not prima facie evidence of an historical connection, as many cultures have independently recorded numbers as collections of strokes. With a similar writing instrument, the cursive forms of such groups of strokes could be broadly similar as well, this is one of the primary hypotheses for the origin of Brahmi numerals. Another possibility is that the numerals were acrophonic, like the Attic numerals, based on the Kharoṣṭhī alphabet. For instance, chatur 4 early on took a ¥ shape much like the Kharosthi letter ch. However, there are problems of lack of records; the full set of numerals is not attested until 400 years after Ashoka. Assertions that either the numerals derive from tallies or that they are alphabetic are, at best, educated guesses. Brahmi script Georges Ifrah, The Universal History of Numbers: From Prehistory to the Invention of the Computer.
Translated by David Bellos, Sophie Wood, pub. J. Wiley, 2000. Karl Menninger, Number Words and Number Symbols - A Cultural History of Numbers ISBN 0-486-27096-3 David Eugene Smith and Louis Charles Karpinski, The Hindu-Arabic Numerals
The system of Hebrew numerals is a quasi-decimal alphabetic numeral system using the letters of the Hebrew alphabet. The system was adapted from that of the Greek numerals in the late 2nd century BCE; the current numeral system is known as the Hebrew alphabetic numerals to contrast with earlier systems of writing numerals used in classical antiquity. These systems were inherited from usage in the Aramaic and Phoenician scripts, attested from c. 800 BC in the so-called Samaria ostraca and sometimes known as Hebrew-Aramaic numerals derived from the Egyptian Hieratic numerals. The Greek system was adopted in Hellenistic Judaism and had been in use in Greece since about the 5th century BC. In this system, there is no notation for zero, the numeric values for individual letters are added together; each unit is assigned a separate letter, each tens a separate letter, the first four hundreds a separate letter. The hundreds are represented by the sum of two or three letters representing the first four hundreds.
To represent numbers from 1,000 to 999,999, the same letters are reused to serve as thousands, tens of thousands, hundreds of thousands. Gematria uses these transformations extensively. In Israel today, the decimal system of Arabic numerals is used in all cases; the Hebrew numerals are used only in special cases, such as when using the Hebrew calendar, or numbering a list, much as Roman numerals are used in the West. The Hebrew language has names for common numbers. Letters of the Hebrew alphabet are used to represent numbers in a few traditional contexts, for example in calendars. In other situations Arabic numerals are used. Cardinal and ordinal numbers must agree in gender with the noun. If there is no such noun, the feminine form is used. For ordinal numbers greater than ten the cardinal is used and numbers above the value 20 have no gender. Note: For ordinal numbers greater than 10, cardinal numbers are used instead. Note: For numbers greater than 20, gender does not apply. Numbers greater than million were represented by the long scale.
Cardinal and ordinal numbers must agree in gender with the noun. If there is no such noun, the feminine form is used. Ordinal numbers must agree in number and definite status like other adjectives; the cardinal number precedes the noun, except for the number one. The number two is special: shnayim and shtayim become shney and shtey when followed by the noun they count. For ordinal numbers greater than ten the cardinal is used; the Hebrew numeric system operates on the additive principle in which the numeric values of the letters are added together to form the total. For example, 177 is represented as קעז which corresponds to 100 + 70 + 7 = 177. Mathematically, this type of system requires 27 letters. In practice the last letter, tav is used in combination with itself and/or other letters from kof onwards, to generate numbers from 500 and above. Alternatively, the 22-letter Hebrew numeral set is sometimes extended to 27 by using 5 sofit forms of the Hebrew letters. By convention, the numbers 15 and 16 are represented as ט״ו and ט״ז in order to refrain from using the two-letter combinations י-ה and י-ו, which are alternate written forms for the Name of God in everyday writing.
In the calendar, this manifests every full moon. Combinations which would spell out words with negative connotations are sometimes avoided by switching the order of the letters. For instance, 744 which should be written as תשמ״ד might instead be written as תשד״מ or תמש״ד; the Hebrew numeral system has sometimes been extended to include the five final letter forms—ך, ם, ן, ף and ץ —which are used to indicate the numbers from 500 to 900. The ordinary forms for 500 to 900 are: ת״ק, ת״ר, ת״ש, ת״ת and תת״ק. Gershayim are inserted before the last letter to indicate that the sequence of letters represents a number rather than a word; this is used in the case. A single Geresh is appended after a single letter to indicate that the letter represents a number rather than a word; this is used in the case. Note that Geresh and Gershayim indicate "not a word." Context determines whether they indicate a number or something else. An alternative method found in old manuscripts and still found on modern-day tombstones is to put a dot above each letter of the number.
In print, Arabic numerals are emplo