History of large numbers

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Different cultures used different traditional numeral systems for naming large numbers. The extent of large numbers used varied in each culture.

One interesting point in using large numbers is the confusion on the term billion and milliard in many countries, and the use of zillion to denote a very large number where precision is not required.


Ancient India

The Indians had a passion for high numbers, which is intimately related to their religious thought. For example, in texts belonging to the Vedic literature, we find individual Sanskrit names for each of the powers of 10 up to a trillion and even 1062. (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 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.

The Lalitavistara Sutra (a Mahayana Buddhist work) recounts a contest including writing, arithmetic, wrestling and archery, in which the 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 1053, 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 10421, that is, a 1 followed by 421 zeros.

There is also an analogous system of Sanskrit terms for fractional numbers, capable of dealing with both very large and very small numbers.

Larger number in Buddhism works up to Bukeshuo bukeshuo zhuan (不可說不可說轉) 10^{7\times 2^{122}} or 1037218383881977644441306597687849648128, which appeared as Bodhisattva's maths in the Avataṃsaka Sūtra.[1][2], though chapter 30 (the Asamkyeyas) in Thomas Cleary's translation of it we find the definition of the number "untold" as exactly 1010*2122, expanded in the 2nd verses to 1045*2121 and continuing a similar expansion indeterminately.

A few large numbers used in India by about 5th century BCE (See Georges Ifrah: A Universal History of Numbers, pp 422–423):

  • koti —107
  • ayuta —109
  • niyuta —1011
  • kankara —1013
  • pakoti —1014
  • vivara —1015
  • kshobhya —1017
  • vivaha —1019
  • kotippakoti —1021
  • bahula —1023
  • nagabala —1025
  • nahuta —1028
  • titlambha —1029
  • vyavasthanapajnapati —1031
  • hetuhila —1033
  • ninnahuta —1035
  • hetvindriya —1037
  • samaptalambha —1039
  • gananagati —1041
  • akkhobini —1042
  • niravadya —1043
  • mudrabala —1045
  • sarvabala —1047
  • bindu —1049
  • sarvajna —1051
  • vibhutangama —1053
  • abbuda —1056
  • nirabbuda —1063
  • ahaha —1070
  • ababa —1077
  • atata —1084
  • soganghika —1091
  • uppala —1098
  • kumuda —10105
  • pundarika —10112
  • paduma —10119
  • kathana —10126
  • mahakathana —10133
  • asankheya —10140
  • dhvajagranishamani —10421

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