1.
12 (number)
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12 is the natural number following 11 and preceding 13. The product of the first three factorials, twelve is a highly composite number, divisible by 2,3,4. It is central to systems of counting, including the Western calendar and units of time. The word twelve is the largest number with a name in English. Such uses gradually disappeared with the introduction of Arabic numerals during the 12th-century Renaissance and it derives from the Old English twelf and tuelf, first attested in the 10th-century Lindisfarne Gospels Book of John. It has cognates in every Germanic language, whose Proto-Germanic ancestor has been reconstructed as *twaliƀi, from *twa and suffix *-lif- or *-liƀ- of uncertain meaning. It is sometimes compared with the Lithuanian dvýlika, although -lika is used as the suffix for all numbers from 11 to 19, every other Indo-European language instead uses a form of two+ten, such as the Latin duōdecim. The usual ordinal form is twelfth but dozenth or duodecimal is also used in some contexts, similarly, a group of twelve things is usually a dozen but may also be referred to as a duodecad. The adjective referring to a group of twelve is duodecuple, as with eleven, the earliest forms of twelve are often considered to be connected with Proto-Germanic *liƀan or *liƀan, with the implicit meaning that two is left after having already counted to ten. The Lithuanian suffix is also considered to share a similar development, the suffix *-lif- has also been connected with reconstructions of the Proto-Germanic for ten. While, as mentioned above,12 has its own name in Germanic languages such as English and German, it is a number in many other languages, e. g. Italian dodici. In Germany, according to an old tradition, the numbers 0 through 12 were spelt out, the Duden now calls this tradition outdated and no longer valid, but many writers still follow it. Another system spells out all numbers written in one or two words, Twelve is a composite number, the smallest number with exactly six divisors, its divisors being 1,2,3,4,6 and 12. Twelve is also a composite number, the next one being twenty-four. Twelve is also a highly composite number, the next one being sixty. It is the first composite number of the form p2q, a square-prime,12 has an aliquot sum of 16. Accordingly,12 is the first abundant number and demonstrates an 8-member aliquot sequence,12 is the 3rd composite number in the 3-aliquot tree, the only number which has 12 as its aliquot sum is the square 121. Only 2 other square primes are abundant, Twelve is a sublime number, a number that has a perfect number of divisors, and the sum of its divisors is also a perfect number
2.
Moon
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The Moon is an astronomical body that orbits planet Earth, being Earths only permanent natural satellite. It is the fifth-largest natural satellite in the Solar System, following Jupiters satellite Io, the Moon is second-densest satellite among those whose densities are known. The average distance of the Moon from the Earth is 384,400 km, the Moon is thought to have formed about 4.51 billion years ago, not long after Earth. It is the second-brightest regularly visible celestial object in Earths sky, after the Sun and its surface is actually dark, although compared to the night sky it appears very bright, with a reflectance just slightly higher than that of worn asphalt. Its prominence in the sky and its cycle of phases have made the Moon an important cultural influence since ancient times on language, calendars, art. The Moons gravitational influence produces the ocean tides, body tides, and this matching of apparent visual size will not continue in the far future. The Moons linear distance from Earth is currently increasing at a rate of 3.82 ±0.07 centimetres per year, since the Apollo 17 mission in 1972, the Moon has been visited only by uncrewed spacecraft. The usual English proper name for Earths natural satellite is the Moon, the noun moon is derived from moone, which developed from mone, which is derived from Old English mōna, which ultimately stems from Proto-Germanic *mǣnōn, like all Germanic language cognates. Occasionally, the name Luna is used, in literature, especially science fiction, Luna is used to distinguish it from other moons, while in poetry, the name has been used to denote personification of our moon. The principal modern English adjective pertaining to the Moon is lunar, a less common adjective is selenic, derived from the Ancient Greek Selene, from which is derived the prefix seleno-. Both the Greek Selene and the Roman goddess Diana were alternatively called Cynthia, the names Luna, Cynthia, and Selene are reflected in terminology for lunar orbits in words such as apolune, pericynthion, and selenocentric. The name Diana is connected to dies meaning day, several mechanisms have been proposed for the Moons formation 4.51 billion years ago, and some 60 million years after the origin of the Solar System. These hypotheses also cannot account for the angular momentum of the Earth–Moon system. This hypothesis, although not perfect, perhaps best explains the evidence, eighteen months prior to an October 1984 conference on lunar origins, Bill Hartmann, Roger Phillips, and Jeff Taylor challenged fellow lunar scientists, You have eighteen months. Go back to your Apollo data, go back to computer, do whatever you have to. Dont come to our conference unless you have something to say about the Moons birth, at the 1984 conference at Kona, Hawaii, the giant impact hypothesis emerged as the most popular. Afterward there were only two groups, the giant impact camp and the agnostics. Giant impacts are thought to have been common in the early Solar System, computer simulations of a giant impact have produced results that are consistent with the mass of the lunar core and the present angular momentum of the Earth–Moon system
3.
Month
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A month is a unit of time, used with calendars, which is approximately as long as a natural period related to the motion of the Moon, month and Moon are cognates. The traditional concept arose with the cycle of phases, such months are synodic months. From excavated tally sticks, researchers have deduced that people counted days in relation to the Moons phases as early as the Paleolithic age. Synodic months, based on the Moons orbital period with respect to the Earth-Sun line, are still the basis of many calendars today, the following types of months are mainly of significance in astronomy, most of them first recognized in Babylonian lunar astronomy. The sidereal month is defined as the Moons orbital period in a frame of reference. The exact duration of the period cannot be easily determined. However, it is equal to the time it takes the Moon to pass twice a fixed star. A synodic month is the most familiar lunar cycle, defined as the interval between two consecutive occurrences of a particular phase as seen by an observer on Earth. The mean length of the month is 29.53059 days. Due to the eccentricity of the orbit around Earth, the length of a synodic month can vary by up to seven hours. The tropical month is the time for the Moon to pass twice through the same equinox point of the sky. It is 27.32158 days, very slightly shorter than the sidereal month days, unlike the sidereal month, it can be measured precisely. An anomalistic month is the time the Moon takes to go from perigee to perigee - the point in the Moons orbit when it is closest to Earth. An anomalistic month is about 27.55455 days on average and its duration is about 27.21222 days on average. A synodic month is longer than a month because the Earth-Moon system is orbiting the Sun in the same direction as the Moon is orbiting the Earth. The Sun moves eastward with respect to the stars and it takes about 2.2 days longer for the Moon to return to the apparent position with respect to the Sun. An anomalistic month is longer than a month because the perigee moves in the same direction as the Moon is orbiting the Earth. Therefore, the Moon takes a longer to return to perigee than to return to the same star
4.
Sun
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The Sun is the star at the center of the Solar System. It is a perfect sphere of hot plasma, with internal convective motion that generates a magnetic field via a dynamo process. It is by far the most important source of energy for life on Earth. Its diameter is about 109 times that of Earth, and its mass is about 330,000 times that of Earth, accounting for about 99. 86% of the total mass of the Solar System. About three quarters of the Suns mass consists of hydrogen, the rest is mostly helium, with smaller quantities of heavier elements, including oxygen, carbon, neon. The Sun is a G-type main-sequence star based on its spectral class and it formed approximately 4.6 billion years ago from the gravitational collapse of matter within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into a disk that became the Solar System. The central mass became so hot and dense that it eventually initiated nuclear fusion in its core and it is thought that almost all stars form by this process. The Sun is roughly middle-aged, it has not changed dramatically for more than four billion years and it is calculated that the Sun will become sufficiently large enough to engulf the current orbits of Mercury, Venus, and probably Earth. The enormous effect of the Sun on Earth has been recognized since prehistoric times, the synodic rotation of Earth and its orbit around the Sun are the basis of the solar calendar, which is the predominant calendar in use today. The English proper name Sun developed from Old English sunne and may be related to south, all Germanic terms for the Sun stem from Proto-Germanic *sunnōn. The English weekday name Sunday stems from Old English and is ultimately a result of a Germanic interpretation of Latin dies solis, the Latin name for the Sun, Sol, is not common in general English language use, the adjectival form is the related word solar. The term sol is used by planetary astronomers to refer to the duration of a solar day on another planet. A mean Earth solar day is approximately 24 hours, whereas a mean Martian sol is 24 hours,39 minutes, and 35.244 seconds. From at least the 4th Dynasty of Ancient Egypt, the Sun was worshipped as the god Ra, portrayed as a falcon-headed divinity surmounted by the solar disk, and surrounded by a serpent. In the New Empire period, the Sun became identified with the dung beetle, in the form of the Sun disc Aten, the Sun had a brief resurgence during the Amarna Period when it again became the preeminent, if not only, divinity for the Pharaoh Akhenaton. The Sun is viewed as a goddess in Germanic paganism, Sól/Sunna, in ancient Roman culture, Sunday was the day of the Sun god. It was adopted as the Sabbath day by Christians who did not have a Jewish background, the symbol of light was a pagan device adopted by Christians, and perhaps the most important one that did not come from Jewish traditions
5.
Year
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A year is the orbital period of the Earth moving in its orbit around the Sun. Due to the Earths axial tilt, the course of a year sees the passing of the seasons, marked by changes in weather, the hours of daylight, and, consequently, vegetation and soil fertility. In temperate and subpolar regions around the globe, four seasons are recognized, spring, summer, autumn. In tropical and subtropical regions several geographical sectors do not present defined seasons, but in the seasonal tropics, a calendar year is an approximation of the number of days of the Earths orbital period as counted in a given calendar. The Gregorian, or modern, calendar, presents its calendar year to be either a common year of 365 days or a year of 366 days, as do the Julian calendars. For the Gregorian calendar the average length of the year across the complete leap cycle of 400 years is 365.2425 days. The ISO standard ISO 80000-3, Annex C, supports the symbol a to represent a year of either 365 or 366 days, in English, the abbreviations y and yr are commonly used. In astronomy, the Julian year is a unit of time, it is defined as 365.25 days of exactly 86400 seconds, totalling exactly 31557600 seconds in the Julian astronomical year. The word year is used for periods loosely associated with, but not identical to, the calendar or astronomical year, such as the seasonal year, the fiscal year. Similarly, year can mean the period of any planet, for example. The term can also be used in reference to any long period or cycle, west Saxon ġēar, Anglian ġēr continues Proto-Germanic *jǣran. Cognates are German Jahr, Old High German jār, Old Norse ár and Gothic jer, all the descendants of the Proto-Indo-European noun *yeh₁rom year, season. Cognates also descended from the same Proto-Indo-European noun are Avestan yārǝ year, Greek ὥρα year, season, period of time, Old Church Slavonic jarŭ, Latin annus is from a PIE noun *h₂et-no-, which also yielded Gothic aþn year. Both *yeh₁-ro- and *h₂et-no- are based on verbal roots expressing movement, *h₁ey- and *h₂et- respectively, the Greek word for year, ἔτος, is cognate with Latin vetus old, from the PIE word *wetos- year, also preserved in this meaning in Sanskrit vat-sa- yearling and vat-sa-ras year. Derived from Latin annus are a number of English words, such as annual, annuity, anniversary, etc. per annum means each year, anno Domini means in the year of the Lord. No astronomical year has an number of days or lunar months. Financial and scientific calculations often use a 365-day calendar to simplify daily rates, in the Julian calendar, the average length of a year is 365.25 days. In a non-leap year, there are 365 days, in a year there are 366 days
6.
Divisor
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In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some other integer to produce n. In this case one says also that n is a multiple of m, an integer n is divisible by another integer m if m is a divisor of n, this implies dividing n by m leaves no remainder. Under this definition, the statement m ∣0 holds for every m, as before, but with the additional constraint k ≠0. Under this definition, the statement m ∣0 does not hold for m ≠0, in the remainder of this article, which definition is applied is indicated where this is significant. Divisors can be negative as well as positive, although sometimes the term is restricted to positive divisors. For example, there are six divisors of 4, they are 1,2,4, −1, −2, and −4,1 and −1 divide every integer. Every integer is a divisor of itself, every integer is a divisor of 0. Integers divisible by 2 are called even, and numbers not divisible by 2 are called odd,1, −1, n and −n are known as the trivial divisors of n. A divisor of n that is not a divisor is known as a non-trivial divisor. A non-zero integer with at least one divisor is known as a composite number, while the units −1 and 1. There are divisibility rules which allow one to recognize certain divisors of a number from the numbers digits, the generalization can be said to be the concept of divisibility in any integral domain. 7 is a divisor of 42 because 7 ×6 =42 and it can also be said that 42 is divisible by 7,42 is a multiple of 7,7 divides 42, or 7 is a factor of 42. The non-trivial divisors of 6 are 2, −2,3, the positive divisors of 42 are 1,2,3,6,7,14,21,42. 5 ∣0, because 5 ×0 =0, if a ∣ b and b ∣ a, then a = b or a = − b. If a ∣ b and a ∣ c, then a ∣ holds, however, if a ∣ b and c ∣ b, then ∣ b does not always hold. If a ∣ b c, and gcd =1, then a ∣ c, if p is a prime number and p ∣ a b then p ∣ a or p ∣ b. A positive divisor of n which is different from n is called a proper divisor or a part of n. A number that does not evenly divide n but leaves a remainder is called an aliquant part of n, an integer n >1 whose only proper divisor is 1 is called a prime number
7.
Duodecimal
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The duodecimal system is a positional notation numeral system using twelve as its base. In this system, the number ten may be written by a rotated 2 and this notation was introduced by Sir Isaac Pitman. These digit forms are available as Unicode characters on computerized systems since June 2015 as ↊ and ↋, other notations use A, T, or X for ten and B or E for eleven. The number twelve is written as 10 in duodecimal, whereas the digit string 12 means 1 dozen and 2 units. Similarly, in duodecimal 100 means 1 gross,1000 means 1 great gross, the number twelve, a superior highly composite number, is the smallest number with four non-trivial factors, and the smallest to include as factors all four numbers within the subitizing range. As a result, duodecimal has been described as the number system. Of its factors,2 and 3 are prime, which means the reciprocals of all 3-smooth numbers have a representation in duodecimal. In particular, the five most elementary fractions all have a terminating representation in duodecimal. This all makes it a convenient number system for computing fractions than most other number systems in common use, such as the decimal, vigesimal, binary. Although the trigesimal and sexagesimal systems do even better in respect, this is at the cost of unwieldy multiplication tables. In this section, numerals are based on decimal places, for example,10 means ten,12 means twelve. Languages using duodecimal number systems are uncommon, germanic languages have special words for 11 and 12, such as eleven and twelve in English. However, they are considered to come from Proto-Germanic *ainlif and *twalif, historically, units of time in many civilizations are duodecimal. There are twelve signs of the zodiac, twelve months in a year, traditional Chinese calendars, clocks, and compasses are based on the twelve Earthly Branches. There are 12 inches in a foot,12 troy ounces in a troy pound,12 old British pence in a shilling,24 hours in a day. The Romans used a system based on 12, including the uncia which became both the English words ounce and inch. The importance of 12 has been attributed to the number of cycles in a year. It is possible to count to 12 with the acting as a pointer
8.
Mesopotamia
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In the Iron Age, it was controlled by the Neo-Assyrian and Neo-Babylonian Empires. The Sumerians and Akkadians dominated Mesopotamia from the beginning of history to the fall of Babylon in 539 BC. It fell to Alexander the Great in 332 BC, and after his death, around 150 BC, Mesopotamia was under the control of the Parthian Empire. Mesopotamia became a battleground between the Romans and Parthians, with parts of Mesopotamia coming under ephemeral Roman control. In AD226, eastern part of it fell to the Sassanid Persians, division of Mesopotamia between Roman and Sassanid Empires lasted until the 7th century Muslim conquest of Persia of the Sasanian Empire and Muslim conquest of the Levant from Byzantines. A number of primarily neo-Assyrian and Christian native Mesopotamian states existed between the 1st century BC and 3rd century AD, including Adiabene, Osroene, and Hatra, Mesopotamia is the site of the earliest developments of the Neolithic Revolution from around 10,000 BC. The regional toponym Mesopotamia comes from the ancient Greek root words μέσος middle and ποταμός river and it is used throughout the Greek Septuagint to translate the Hebrew equivalent Naharaim. In the Anabasis, Mesopotamia was used to designate the land east of the Euphrates in north Syria, the Aramaic term biritum/birit narim corresponded to a similar geographical concept. The neighbouring steppes to the west of the Euphrates and the part of the Zagros Mountains are also often included under the wider term Mesopotamia. A further distinction is made between Northern or Upper Mesopotamia and Southern or Lower Mesopotamia. Upper Mesopotamia, also known as the Jazira, is the area between the Euphrates and the Tigris from their sources down to Baghdad, Lower Mesopotamia is the area from Baghdad to the Persian Gulf and includes Kuwait and parts of western Iran. In modern academic usage, the term Mesopotamia often also has a chronological connotation and it is usually used to designate the area until the Muslim conquests, with names like Syria, Jazirah, and Iraq being used to describe the region after that date. It has been argued that these later euphemisms are Eurocentric terms attributed to the region in the midst of various 19th-century Western encroachments, Mesopotamia encompasses the land between the Euphrates and Tigris rivers, both of which have their headwaters in the Armenian Highlands. Both rivers are fed by tributaries, and the entire river system drains a vast mountainous region. Overland routes in Mesopotamia usually follow the Euphrates because the banks of the Tigris are frequently steep and difficult. The climate of the region is semi-arid with a vast desert expanse in the north which gives way to a 15,000 square kilometres region of marshes, lagoons, mud flats, in the extreme south, the Euphrates and the Tigris unite and empty into the Persian Gulf. In the marshlands to the south of the area, a complex water-borne fishing culture has existed since prehistoric times, periodic breakdowns in the cultural system have occurred for a number of reasons. Alternatively, military vulnerability to invasion from marginal hill tribes or nomadic pastoralists has led to periods of trade collapse and these trends have continued to the present day in Iraq
9.
120 (number)
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120, read as one hundred twenty, is the natural number following 119 and preceding 121. In English and other Germanic languages, it was formerly known as one hundred. This hundred of six score is now obsolete, but is described as the hundred or great hundred in historical contexts. 120 is the factorial of 5, and the sum of a twin prime pair,120 is the sum of four consecutive prime numbers, four consecutive powers of 2, and four consecutive powers of 3. It is also a sparsely totient number,120 is the smallest number to appear six times in Pascals triangle. 120 is also the smallest multiple of 6 with no adjacent prime number and it is the eighth hexagonal number and the fifteenth triangular number, as well as the sum of the first eight triangular numbers, making it also a tetrahedral number. 120 is divisible by the first 5 triangular numbers and the first 4 tetrahedral numbers,120 is the first multiply perfect number of order three. The sum of its factors sum to 360, exactly three times 120, note that perfect numbers are order two by the same definition. 120 is divisible by the number of primes below it,30 in this case, however, there is no integer which has 120 as the sum of its proper divisors, making 120 an untouchable number. The sum of Eulers totient function φ over the first nineteen integers is 120,120 figures in Pierre de Fermats modified Diophantine problem as the largest known integer of the sequence 1,3,8,120. Fermat wanted to another positive integer that multiplied with any of the other numbers in the sequence yields a number that is one less than a square. Leonhard Euler also searched for this number, but failed to find it, the internal angles of a regular hexagon are all 120 degrees. 120 is a Harshad number in base 10,120 is the atomic number of Unbinilium, an element yet to be discovered. The cubits of the height of the Temple building The age at which Moses died, in astrology, when two planets in a persons chart are 120 degrees apart from each other, this is called a trine. This is supposed to bring luck in the persons life. The height in inches of a hoop in the National Basketball Association. 120 is also, The medical telephone number in China In Austria, in the US Army, a common diameter for a mortar in mm. TT scale, a scale for model trains, is 1,120. 120 film is a medium format film developed by Kodak,120, a 2008 Turkish film The Israeli national legislature, the Knesset, has 120 seats
10.
10 (number)
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10 is an even natural number following 9 and preceding 11. Ten is the base of the numeral system, by far the most common system of denoting numbers in both spoken and written language. The reason for the choice of ten is assumed to be that humans have ten fingers, a collection of ten items is called a decade. The ordinal adjective is decimal, the adjective is denary. Increasing a quantity by one order of magnitude is most widely understood to mean multiplying the quantity by ten, to reduce something by one tenth is to decimate. A theoretical highest number in topics that require a rating, by contrast having 0 or 1 as the lowest number, Ten is a composite number, its proper divisors being 1,2 and 5. Ten is the smallest noncototient, a number that cannot be expressed as the difference between any integer and the number of coprimes below it. Ten is the discrete semiprime and the second member of the discrete semiprime family. Ten has an aliquot sum σ of 8 and is accordingly the first discrete semiprime to be in deficit, all subsequent discrete semiprimes are in deficit. The aliquot sequence for 10 comprises five members with this number being the second member of the 7-aliquot tree. Ten is the smallest semiprime that is the sum of all the prime numbers from its lower factor through its higher factor Only three other small semiprimes share this attribute. It is the sum of only one number the discrete semiprime 14. Ten is the sum of the first three numbers, of the four first numbers, of the square of the two first odd numbers and also of the first four factorials. Ten is the eighth Perrin number, preceded in the sequence by 5,5,7, a polygon with ten sides is a decagon, and 10 is a decagonal number. Because 10 is the product of a power of 2 with nothing but distinct Fermat primes, Ten is also a triangular number, a centered triangular number, and a tetrahedral number. Ten is the number of n queens problem solutions for n =5, Ten is the smallest number whose status as a possible friendly number is unknown. As is the case for any base in its system, ten is the first two-digit number in decimal, any integer written in the decimal system can be multiplied by ten by adding a zero to the end. The Roman numeral for ten is X, it is thought that the V for five is derived from an open hand, incidentally, the Chinese word numeral for ten, is also a cross, 十
11.
French language
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French is a Romance language of the Indo-European family. It descended from the Vulgar Latin of the Roman Empire, as did all Romance languages, French has evolved from Gallo-Romance, the spoken Latin in Gaul, and more specifically in Northern Gaul. Its closest relatives are the other langues doïl—languages historically spoken in northern France and in southern Belgium, French was also influenced by native Celtic languages of Northern Roman Gaul like Gallia Belgica and by the Frankish language of the post-Roman Frankish invaders. Today, owing to Frances past overseas expansion, there are numerous French-based creole languages, a French-speaking person or nation may be referred to as Francophone in both English and French. French is a language in 29 countries, most of which are members of la francophonie. As of 2015, 40% of the population is in Europe, 35% in sub-Saharan Africa, 15% in North Africa and the Middle East, 8% in the Americas. French is the fourth-most widely spoken mother tongue in the European Union, 1/5 of Europeans who do not have French as a mother tongue speak French as a second language. As a result of French and Belgian colonialism from the 17th and 18th century onward, French was introduced to new territories in the Americas, Africa, most second-language speakers reside in Francophone Africa, in particular Gabon, Algeria, Mauritius, Senegal and Ivory Coast. In 2015, French was estimated to have 77 to 110 million native speakers, approximately 274 million people are able to speak the language. The Organisation internationale de la Francophonie estimates 700 million by 2050, in 2011, Bloomberg Businessweek ranked French the third most useful language for business, after English and Standard Mandarin Chinese. Under the Constitution of France, French has been the language of the Republic since 1992. France mandates the use of French in official government publications, public education except in specific cases, French is one of the four official languages of Switzerland and is spoken in the western part of Switzerland called Romandie, of which Geneva is the largest city. French is the language of about 23% of the Swiss population. French is also a language of Luxembourg, Monaco, and Aosta Valley, while French dialects remain spoken by minorities on the Channel Islands. A plurality of the worlds French-speaking population lives in Africa and this number does not include the people living in non-Francophone African countries who have learned French as a foreign language. Due to the rise of French in Africa, the total French-speaking population worldwide is expected to reach 700 million people in 2050, French is the fastest growing language on the continent. French is mostly a language in Africa, but it has become a first language in some urban areas, such as the region of Abidjan, Ivory Coast and in Libreville. There is not a single African French, but multiple forms that diverged through contact with various indigenous African languages, sub-Saharan Africa is the region where the French language is most likely to expand, because of the expansion of education and rapid population growth
12.
Cardinal number
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In mathematics, cardinal numbers, or cardinals for short, are a generalization of the natural numbers used to measure the cardinality of sets. The cardinality of a set is a natural number, the number of elements in the set. The transfinite cardinal numbers describe the sizes of infinite sets, cardinality is defined in terms of bijective functions. Two sets have the same cardinality if, and only if, in the case of finite sets, this agrees with the intuitive notion of size. In the case of sets, the behavior is more complex. It is also possible for a subset of an infinite set to have the same cardinality as the original set. There is a sequence of cardinal numbers,0,1,2,3, …, n, …, ℵ0, ℵ1, ℵ2, …, ℵ α, …. This sequence starts with the natural numbers including zero, which are followed by the aleph numbers, the aleph numbers are indexed by ordinal numbers. Under the assumption of the axiom of choice, this transfinite sequence includes every cardinal number, If one rejects that axiom, the situation is more complicated, with additional infinite cardinals that are not alephs. Cardinality is studied for its own sake as part of set theory and it is also a tool used in branches of mathematics including model theory, combinatorics, abstract algebra, and mathematical analysis. In category theory, the numbers form a skeleton of the category of sets. The notion of cardinality, as now understood, was formulated by Georg Cantor, cardinality can be used to compare an aspect of finite sets, e. g. the sets and are not equal, but have the same cardinality, namely three. Cantor applied his concept of bijection to infinite sets, e. g. the set of natural numbers N =, thus, all sets having a bijection with N he called denumerable sets and they all have the same cardinal number. This cardinal number is called ℵ0, aleph-null and he called the cardinal numbers of these infinite sets transfinite cardinal numbers. Cantor proved that any unbounded subset of N has the same cardinality as N and he later proved that the set of all real algebraic numbers is also denumerable. His proof used an argument with nested intervals, but in an 1891 paper he proved the result using his ingenious. The new cardinal number of the set of numbers is called the cardinality of the continuum. His continuum hypothesis is the proposition that c is the same as ℵ1 and this hypothesis has been found to be independent of the standard axioms of mathematical set theory, it can neither be proved nor disproved from the standard assumptions
13.
Latin
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Latin is a classical language belonging to the Italic branch of the Indo-European languages. The Latin alphabet is derived from the Etruscan and Greek alphabets, Latin was originally spoken in Latium, in the Italian Peninsula. Through the power of the Roman Republic, it became the dominant language, Vulgar Latin developed into the Romance languages, such as Italian, Portuguese, Spanish, French, and Romanian. Latin, Italian and French have contributed many words to the English language, Latin and Ancient Greek roots are used in theology, biology, and medicine. By the late Roman Republic, Old Latin had been standardised into Classical Latin, Vulgar Latin was the colloquial form spoken during the same time and attested in inscriptions and the works of comic playwrights like Plautus and Terence. Late Latin is the language from the 3rd century. Later, Early Modern Latin and Modern Latin evolved, Latin was used as the language of international communication, scholarship, and science until well into the 18th century, when it began to be supplanted by vernaculars. Ecclesiastical Latin remains the language of the Holy See and the Roman Rite of the Catholic Church. Today, many students, scholars and members of the Catholic clergy speak Latin fluently and it is taught in primary, secondary and postsecondary educational institutions around the world. The language has been passed down through various forms, some inscriptions have been published in an internationally agreed, monumental, multivolume series, the Corpus Inscriptionum Latinarum. Authors and publishers vary, but the format is about the same, volumes detailing inscriptions with a critical apparatus stating the provenance, the reading and interpretation of these inscriptions is the subject matter of the field of epigraphy. The works of several hundred ancient authors who wrote in Latin have survived in whole or in part and they are in part the subject matter of the field of classics. The Cat in the Hat, and a book of fairy tales, additional resources include phrasebooks and resources for rendering everyday phrases and concepts into Latin, such as Meissners Latin Phrasebook. The Latin influence in English has been significant at all stages of its insular development. From the 16th to the 18th centuries, English writers cobbled together huge numbers of new words from Latin and Greek words, dubbed inkhorn terms, as if they had spilled from a pot of ink. Many of these words were used once by the author and then forgotten, many of the most common polysyllabic English words are of Latin origin through the medium of Old French. Romance words make respectively 59%, 20% and 14% of English, German and those figures can rise dramatically when only non-compound and non-derived words are included. Accordingly, Romance words make roughly 35% of the vocabulary of Dutch, Roman engineering had the same effect on scientific terminology as a whole
14.
Spanish language
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Spanish —also called Castilian —is a Romance language that originated in the Castile region of Spain, with hundreds of millions of native speakers around the world. It is usually considered the worlds second-most spoken native language after Mandarin Chinese and it is one of the few languages to use inverted question and exclamation marks. Spanish is a part of the Ibero-Romance group of languages, which evolved from several dialects of Vulgar Latin in Iberia after the collapse of the Western Roman Empire in the 5th century. Beginning in the early 16th century, Spanish was taken to the colonies of the Spanish Empire, most notably to the Americas, as well as territories in Africa, Oceania, around 75% of modern Spanish is derived from Latin. Greek has also contributed substantially to Spanish vocabulary, especially through Latin, Spanish vocabulary has been in contact from an early date with Arabic, having developed during the Al-Andalus era in the Iberian Peninsula. With around 8% of its vocabulary being Arabic in origin, this language is the second most important influence after Latin and it has also been influenced by Basque as well as by neighboring Ibero-Romance languages. It also adopted words from languages such as Gothic language from the Visigoths in which many Spanish names and surnames have a Visigothic origin. Spanish is one of the six languages of the United Nations. It is the language in the world by the number of people who speak it as a mother tongue, after Mandarin Chinese. It is estimated more than 437 million people speak Spanish as a native language. Spanish is the official or national language in Spain, Equatorial Guinea, speakers in the Americas total some 418 million. In the European Union, Spanish is the tongue of 8% of the population. Spanish is the most popular second language learned in the United States, in 2011 it was estimated by the American Community Survey that of the 55 million Hispanic United States residents who are five years of age and over,38 million speak Spanish at home. The Spanish Constitution of 1978 uses the term castellano to define the language of the whole Spanish State in contrast to las demás lenguas españolas. Article III reads as follows, El castellano es la lengua española oficial del Estado, las demás lenguas españolas serán también oficiales en las respectivas Comunidades Autónomas. Castilian is the official Spanish language of the State, the other Spanish languages as well shall be official in their respective Autonomous Communities. The Spanish Royal Academy, on the hand, currently uses the term español in its publications. Two etymologies for español have been suggested, the Spanish Royal Academy Dictionary derives the term from the Provençal word espaignol, and that in turn from the Medieval Latin word Hispaniolus, from—or pertaining to—Hispania
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Francis Grose
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Francis Grose was an English antiquary, draughtsman, and lexicographer. He was born at his fathers house in Broad Street, St-Peter-le-Poer and his parents were Swiss immigrant and jeweller Francis Jacob Grose, and his wife, Anne, daughter of Thomas Bennett of Greenford in Middlesex. Grose was baptized on 11 June 1731 in the parish of St Peter-le-Poer, the eldest of seven children, Francis probably received a classical education but first aimed at a career in the Army. In 1747, he was in Flanders, apparently as a volunteer in Howards regiment of foot, posted to Kent on excise duties in 1750, he met and married Catherine Jordan of Canterbury. They were eventually to have ten children, six of whom survived to adulthood and their eldest son was Francis Grose, the Lieutenant Governor of New South Wales, Australia. Grose left the army in October 1751, possibly to avoid his regiments posting to Scotland, in 1755, his father bought him the post of Richmond Herald but Francis showed little interest in heraldry and was to sell it again in February 1763. In 1757, Grose was elected a member of the Society of Antiquaries, and 1759 he resumed his career, this time in the militia. He was commissioned into the Surrey regiment as a lieutenant, the Surrey militia was disbanded in 1762 but this hardly affected Grose, who continued to receive a salary as paymaster and adjutant even in peacetime. Grose had early on shown a keen interest in drawing, having attempted sketches of buildings as far back as 1749. He was not a gifted draughtsman but he mixed in the London artistic milieu and began to exhibit, first at the Society of Artists in 1767–8. His interest was in the field of medieval remains, which were beginning to exercise an increasing grip on the public imagination, in 1772, he published the first part of The Antiquities of England and Wales, a work which he unashamedly aimed at the popular market. Sometimes the text was taken from books published, or from information supplied by other antiquaries, sometimes Grose collated material himself from which he could work up an article. From 1772 onwards, he toured the country to visit. The fourth and last volume came out in June 1776, and his publishing career was interrupted however, when the Surrey militia was again called into service between 1778 and 1783. This was not an experience for him. Where previously Grose had been able to spend his summers visiting and sketching ancient sites and he did not get on well with his new commanding officer, and he handled regimental finances in a slipshod manner. The result was that he incurred debts towards fellow officers that would take years to straighten out, the financial pressure forced him to increase both the rate and the range of his publications. The Supplement to The Antiquities was resumed in 1783, this time with a proportion of the illustrations being done by other artists
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International Standard Book Number
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The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each edition and variation of a book, for example, an e-book, a paperback and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, the method of assigning an ISBN is nation-based and varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated in 1967 based upon the 9-digit Standard Book Numbering created in 1966, the 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108. Occasionally, a book may appear without a printed ISBN if it is printed privately or the author does not follow the usual ISBN procedure, however, this can be rectified later. Another identifier, the International Standard Serial Number, identifies periodical publications such as magazines, the ISBN configuration of recognition was generated in 1967 in the United Kingdom by David Whitaker and in 1968 in the US by Emery Koltay. The 10-digit ISBN format was developed by the International Organization for Standardization and was published in 1970 as international standard ISO2108, the United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978, an SBN may be converted to an ISBN by prefixing the digit 0. For example, the edition of Mr. J. G. Reeder Returns, published by Hodder in 1965, has SBN340013818 -340 indicating the publisher,01381 their serial number. This can be converted to ISBN 0-340-01381-8, the check digit does not need to be re-calculated, since 1 January 2007, ISBNs have contained 13 digits, a format that is compatible with Bookland European Article Number EAN-13s. An ISBN is assigned to each edition and variation of a book, for example, an ebook, a paperback, and a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned on or after 1 January 2007, a 13-digit ISBN can be separated into its parts, and when this is done it is customary to separate the parts with hyphens or spaces. Separating the parts of a 10-digit ISBN is also done with either hyphens or spaces, figuring out how to correctly separate a given ISBN number is complicated, because most of the parts do not use a fixed number of digits. ISBN issuance is country-specific, in that ISBNs are issued by the ISBN registration agency that is responsible for country or territory regardless of the publication language. Some ISBN registration agencies are based in national libraries or within ministries of culture, in other cases, the ISBN registration service is provided by organisations such as bibliographic data providers that are not government funded. In Canada, ISBNs are issued at no cost with the purpose of encouraging Canadian culture. In the United Kingdom, United States, and some countries, where the service is provided by non-government-funded organisations. Australia, ISBNs are issued by the library services agency Thorpe-Bowker
