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| Different [[culture]]s used different traditional [[numeral system]]s for naming '''large numbers'''. The extent of large numbers used varied in each culture.
| | Optimum Fitness is the name of a fitness studio opened in the city of Sanford, Florida, which offers clients a wide variety of professional services and exercises. Operating in the field of personal training and providing a large number of customized solutions for clients and interested persons, Optimum Fitness has managed to build a great reputation for itself as a very appreciated and sought after facility in the region. The creator and owner of this center is Allen Linville, a local personal trainer with a vast experience in the field gathered over more than 10 years of providing assistance and professional guidance to health and fitness enthusiasts. As a matter of fact, the studio was born from the passion and desire of Allen Linville to create a friendly and efficient environment where he can help clients reach their fitness goals and ultimate heath potential. By going to Optimum Fitness, you will benefit from a wide range of services, which include but do not stop at: weight loss routines, individual training courses, Sanford personal training classes, semi private programs, solutions for age related issues with the health and physical condition, nutrition advice from trained specialists, as well as motivational support during the entire process. The fitness center also has an official website which can be accessed by going online and searching for Optimumfitnessfl.com. The website provides further details about the creator of Optimum Fitness and any other relevant information regarding this facility. <br><br>In addition to this, Optimumfitnessfl.com is a great source of facts and contact details, as well as a direct means of getting in touch with the fitness and exercise specialists working at the center. What sets Optimum Fitness apart from other similar sports facilities in the region is the fact that it focuses on providing individual attention and focused or customized routines to clients, through the large array of solutions which it provides when it comes to [http://goarticles.com/article/9344388 personal fitness training Sanford] has to offer. Optimum Fitness also provides clients, as well as any person interested in starting a fitness routine or weight loss diet, personalized solutions for their particular case, body and condition. By taking into account the current and individual state of health persons are, the experienced personal coaches at Optimum Fitness can design a customized routine which is guaranteed to take into account the particularities of the client’s state of health. Apart from personal training programs, Optimum Fitness also offers semi private solutions and superior quality [http://www.1500dollarwebsite.com/article.php?id=513393 fitness programs]. Other services are the 5-Star Training, the 21 Day Rapid Fat Loss Program, Golf Fitness Report and many more.<br><br>In order to conclude, Optimum Fitness is a reliable, professional and reputable fitness centre dedicated to bringing forward the best personal training Sanford has ever seen. The official website of the gym, Optimumfitnessfl.com, is highly informative and contains multiple pages of information about the services, programs, classes and solutions offered by the experts at Optimum Fitness. Last, but not least, Optimumfitnessfl.com also allows visitors and any Internet user to see past success stories, as well as the story behind the founder of this state of the art fitness facility. |
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| Two interesting points in using large numbers are the confusion on the term [[Long and short scales|billion]] and [[milliard]] in many countries, and the use of ''zillion'' to denote a very large number where precision is not required.
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| ==Ancient India==
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| [[Image:HinduMeasurements.svg|thumb|right|Hindu units of time on a [[logarithmic scale]].]]
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| The [[India]]ns had a passion for high numbers, which is intimately related to their religious thought. For example, in texts belonging to the [[Vedas|Vedic literature]], we find individual [[Sanskrit]] names for ''each'' of the powers of 10 up to a trillion and even 10<sup>62</sup>. (Even today, the words '[[lakh]]' and '[[crore]]', referring to 100,000 and 10,000,000, respectively, are in common use among English-speaking Indians.) One of these [[Vedas|Vedic texts]], the ''[[Yajur Veda]]'', even discusses the concept of numeric [[infinity]] (''purna'' "fullness"), stating that if you subtract ''purna'' from ''purna'', you are still left with ''purna''. | |
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| The ''[[Lalitavistara Sutra]]'' (a [[Mahayana]] [[Buddhism|Buddhist]] work) recounts a contest including writing, arithmetic, wrestling and archery, in which the [[Gautama Buddha|Buddha]] was pitted against the great mathematician Arjuna and showed off his numerical skills by citing the names of the powers of ten up to 1 'tallakshana', which equals 10<sup>53</sup>, but then going on to explain that this is just one of a series of counting systems that can be expanded geometrically. The last number at which he arrived after going through nine successive counting systems was 10<sup>421</sup>, that is, a 1 followed by 421 zeros. | |
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| There is also an analogous system of [[Sanskrit]] terms for fractional numbers, capable of dealing with both very large and very small numbers.
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| Larger number in Buddhism works up to Bukeshuo bukeshuo zhuan (不可說不可說轉) <math>10^{7\times 2^{122}}</math> or 10<sup>37218383881977644441306597687849648128</sup>, which appeared as [[Bodhisattva]]'s maths in the [[Avatamsaka Sutra|Avataṃsaka Sūtra]].,<ref>[http://www.sf.airnet.ne.jp/~ts/language/largenumber.html 無量大数の彼方へ]</ref><ref>[http://www.moroo.com/uzokusou/misc/suumei/suumei.html 大数の名前について]</ref> though chapter 30 (the Asamkyeyas) in Thomas Cleary's translation of it we find the definition of the number "untold" as exactly 10<sup>10*2<sup>122</sup></sup>, expanded in the 2nd verses to 10<sup>45*2<sup>121</sup></sup> and continuing a similar expansion indeterminately.
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| A few large numbers used in India by about 5th century BCE (''See Georges Ifrah: A Universal History of Numbers, pp 422–423''):
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| * ''[[lakh|lakṣá]]'' (लक्ष) —10<sup>5</sup>
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| * ''[[crore|kōṭi]]'' (कोटि) —10<sup>7</sup>
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| * ''ayuta'' (अयुता) —10<sup>9</sup>
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| * ''niyuta'' (नियुता) —10<sup>13</sup>
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| * ''pakoti'' (पकोटि) —10<sup>14</sup>
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| * ''vivara'' (विवारा) —10<sup>15</sup>
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| * ''kshobhya'' (क्षोभ्या) —10<sup>17</sup>
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| * ''vivaha'' (विवाहा) —10<sup>19</sup>
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| * ''kotippakoti'' (कोटिपकोटी) —10<sup>21</sup>
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| * ''bahula'' (बहूला) —10<sup>23</sup>
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| * ''nagabala'' (नागाबाला) —10<sup>25</sup>
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| * ''nahuta'' (नाहूटा) —10<sup>28</sup>
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| * ''titlambha'' (तीतलम्भा) —10<sup>29</sup>
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| * ''vyavasthanapajnapati'' (व्यवस्थानापज्नापति) —10<sup>31</sup>
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| * ''hetuhila'' (हेतुहीला) —10<sup>33</sup>
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| * ''ninnahuta'' (निन्नाहुता) —10<sup>35</sup>
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| * ''hetvindriya'' (हेत्विन्द्रिया) —10<sup>37</sup>
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| * ''samaptalambha'' (समाप्तलम्भा) —10<sup>39</sup>
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| * ''gananagati'' (गनानागती) —10<sup>41</sup>
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| * ''akkhobini'' (अक्खोबिनि) —10<sup>42</sup>
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| * ''niravadya'' (निरावाद्य) —10<sup>43</sup>
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| * ''mudrabala'' (मुद्राबाला) —10<sup>45</sup>
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| * ''sarvabala'' (सर्वबाला) —10<sup>47</sup>
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| * ''bindu'' (बिंदु or बिन्दु) —10<sup>49</sup>
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| * ''sarvajna'' (सर्वज्ञ) —10<sup>51</sup>
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| * ''vibhutangama'' (विभुतन्गमा) —10<sup>53</sup>
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| * ''abbuda'' (अब्बुदा) —10<sup>56</sup>
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| * ''nirabbuda'' (निर्बुद्धा) —10<sup>63</sup>
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| * ''ahaha'' (अहाहा) —10<sup>70</sup>
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| * ''ababa'' (अबाबा). —10<sup>77</sup>
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| * ''atata'' (अटाटा) —10<sup>84</sup>
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| * ''soganghika'' (सोगान्घीका) —10<sup>91</sup>
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| * ''uppala'' (उप्पाला) —10<sup>98</sup>
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| * ''kumuda'' (कुमुदा) —10<sup>105</sup>
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| * ''pundarika'' (पुन्डरीका) —10<sup>112</sup>
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| * ''paduma'' (पद्मा) —10<sup>119</sup>
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| * ''kathana'' (कथाना) —10<sup>126</sup>
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| * ''mahakathana'' (महाकथाना) —10<sup>133</sup>
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| * ''[[asaṃkhyeya]]'' (असंख्येय) —10<sup>140</sup>
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| * ''dhvajagranishamani'' (ध्वजाग्रनिशमनी) —10<sup>421</sup>
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| * ''[[bodhisattva]]'' (बोधिसत्व or बोधिसत्त) —10<sup>37218383881977644441306597687849648128</sup>
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| * ''lalitavistarautra'' (ललितातुलनातारासूत्र) —10<sup>200</sup>infinities
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| * ''[[matsya]]'' (मत्स्य) —10<sup>600</sup>infinities
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| * ''[[kurma]]'' (कुरमा) —10<sup>2000</sup>infinities
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| * ''[[varaha]]'' (वरहा) —10<sup>3600</sup>infinities
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| * ''[[narasimha]]'' (नरसिम्हा) —10<sup>4800</sup>infinities
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| * ''[[vamana]]'' (वामन) —10<sup>5800</sup>infinities
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| * ''[[parashurama]]'' (परशुराम) —10<sup>6000</sup>infinities
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| * ''[[rama]]'' (राम) —10<sup>6800</sup>infinities
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| * ''khrishnaraja'' (कृष्णराज) —10<sup><!-- ?? --></sup>infinities
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| * ''[[kalki]]'' (काईकी or काइकी) —10<sup>8000</sup>infinities
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| * ''[[balarama]]'' (बलराम) —10<sup>9800</sup>infinities
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| * ''[[dasavatara]]'' (दशावतारा) —10<sup>10000</sup>infinities
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| * ''bhagavatapurana'' (भागवतपुराण) —10<sup>18000</sup>infinities
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| * ''avatamsakasutra'' (अवताम्सकासुत्रा) —10<sup>30000</sup>infinities
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| * ''mahadeva'' (महादेव) —10<sup>50000</sup>infinities
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| * ''[[prajapati]]'' (प्रजापति) —10<sup>60000</sup>infinities
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| * ''[[jyotiba]]'' (ज्योतिबा) —10<sup>80000</sup>infinities
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| ==Classical antiquity==
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| In the Western world, specific [[Numeral (linguistics)|number names]] for [[large numbers|larger numbers]] did not come into common use until quite recently. The [[Ancient Greeks]] used a system based on the [[myriad]], that is ten thousand; and their largest named number was a myriad myriad, or one hundred million.
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| In ''[[The Sand Reckoner]]'', [[Archimedes]] (c. 287–212 BC) devised a system of naming large numbers reaching up to
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| :<math>10^{8 \times 10^{16}}</math>,
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| essentially by naming powers of a myriad myriad. This largest number appears because it equals a myriad myriad to the
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| myriad myriadth power, all taken to the myriad myriadth power. This gives a good indication of the notational difficulties encountered by Archimedes, and one can propose that he stopped
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| at this number because he did not devise any new [[ordinal numbers]] (larger than 'myriad myriadth')
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| to match his new [[cardinal numbers]]. Archimedes only used his system up to 10<sup>64</sup>.
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| Archimedes' goal was presumably to name large [[powers of 10]] in order to give rough estimates, but shortly thereafter,
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| [[Apollonius of Perga]] invented a more practical
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| system of naming large numbers which were not powers of 10, based on naming powers of a myriad,
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| for example,
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| :<math> M^{\!\!\!\!\! {}^\beta}</math> would be a myriad squared.
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| Much later, but still in [[classical antiquity|antiquity]], the [[Greek mathematics|Hellenistic mathematician]] [[Diophantus]] (3rd century) used a similar notation to represent large numbers.
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| The Romans, who were less interested in theoretical issues, expressed 1,000,000 as ''decies centena milia'', that is, 'ten hundred thousand'; it was only in the 13th century that the (originally French) word '[[million]]' was introduced .
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| ==Medieval India==
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| The [[India]]ns, who invented the [[numeral system|positional numeral system]], along with [[negative numbers]] and [[0 (number)|zero]], were quite advanced in this aspect. By the 7th century, [[Indian mathematics|Indian mathematicians]] were familiar enough with the notion of infinity as to define it as the quantity whose [[denominator]] is zero. | |
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| ==Modern use of large finite numbers==
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| Far larger finite numbers than any of these occur in modern mathematics. See for instance [[Graham's number]] which is too large to express using [[exponentiation]] or [[Tetration|super exponentiation]]. For more about modern usage for large numbers see [[Large numbers]].
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| == Infinity ==
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| :''Main articles: [[Infinity]] and [[Transfinite number]]''
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| The ultimate in large numbers was, until recently, the concept of [[infinity]], a number defined by being greater than any [[finite set|finite]] number, and used in the mathematical theory of [[limit (mathematics)|limit]]s.
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| However, since the 19th century, mathematicians have studied [[transfinite number]]s, numbers which are not only greater than any finite number, but also, from the viewpoint of [[set theory]], larger than the traditional concept of infinity. Of these transfinite numbers, perhaps the most extraordinary, and arguably, if they exist, "largest", are the [[Large cardinal property|large cardinal]]s. The concept of transfinite numbers, however, was first considered by Indian [[Jain]]a mathematicians as far back as 400 BC.
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| ==References==
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| {{reflist}}
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| ==Further reading==
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| *Georges Ifrah, ''The Universal History of Numbers'', ISBN 1-86046-324-X
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| {{Large numbers}}
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| {{DEFAULTSORT:History Of Large Numbers}}
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| [[Category:Large numbers|*]]
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Optimum Fitness is the name of a fitness studio opened in the city of Sanford, Florida, which offers clients a wide variety of professional services and exercises. Operating in the field of personal training and providing a large number of customized solutions for clients and interested persons, Optimum Fitness has managed to build a great reputation for itself as a very appreciated and sought after facility in the region. The creator and owner of this center is Allen Linville, a local personal trainer with a vast experience in the field gathered over more than 10 years of providing assistance and professional guidance to health and fitness enthusiasts. As a matter of fact, the studio was born from the passion and desire of Allen Linville to create a friendly and efficient environment where he can help clients reach their fitness goals and ultimate heath potential. By going to Optimum Fitness, you will benefit from a wide range of services, which include but do not stop at: weight loss routines, individual training courses, Sanford personal training classes, semi private programs, solutions for age related issues with the health and physical condition, nutrition advice from trained specialists, as well as motivational support during the entire process. The fitness center also has an official website which can be accessed by going online and searching for Optimumfitnessfl.com. The website provides further details about the creator of Optimum Fitness and any other relevant information regarding this facility.
In addition to this, Optimumfitnessfl.com is a great source of facts and contact details, as well as a direct means of getting in touch with the fitness and exercise specialists working at the center. What sets Optimum Fitness apart from other similar sports facilities in the region is the fact that it focuses on providing individual attention and focused or customized routines to clients, through the large array of solutions which it provides when it comes to personal fitness training Sanford has to offer. Optimum Fitness also provides clients, as well as any person interested in starting a fitness routine or weight loss diet, personalized solutions for their particular case, body and condition. By taking into account the current and individual state of health persons are, the experienced personal coaches at Optimum Fitness can design a customized routine which is guaranteed to take into account the particularities of the client’s state of health. Apart from personal training programs, Optimum Fitness also offers semi private solutions and superior quality fitness programs. Other services are the 5-Star Training, the 21 Day Rapid Fat Loss Program, Golf Fitness Report and many more.
In order to conclude, Optimum Fitness is a reliable, professional and reputable fitness centre dedicated to bringing forward the best personal training Sanford has ever seen. The official website of the gym, Optimumfitnessfl.com, is highly informative and contains multiple pages of information about the services, programs, classes and solutions offered by the experts at Optimum Fitness. Last, but not least, Optimumfitnessfl.com also allows visitors and any Internet user to see past success stories, as well as the story behind the founder of this state of the art fitness facility.