History of large numbers
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Different
Indian mathematics
The
- eka (1), daśa (10), mesochi (100), sahasra (1,000), ayuta (10,000), niyuta (100,000), prayuta (1,000,000), arbuda (10,000,000), nyarbuda (100,000,000), saguran (1,000,000,000), madhya (10,000,000,000), anta (100,000,000,000), parârdha (1,000,000,000,000).[1]
Later Hindu and Buddhist texts have extended this list, but these lists are no longer mutually consistent and names of numbers larger than 108 differ between texts.
For example, the Panchavimsha Brahmana lists 109 as nikharva, 1010 vâdava, 1011 akṣiti, while Śâṅkhyâyana Śrauta Sûtra has 109 nikharva, 1010 samudra, 1011 salila, 1012 antya, 1013 ananta. Such lists of names for powers of ten are called daśaguṇottarra saṁjñâ. There area also analogous lists of Sanskrit names for fractional numbers, that is, powers of one tenth.
The
The
The
In modern India, the terms lakh for 105 and crore for 107 are in common use. Both are vernacular (Hindustani) forms derived from a list of names for powers of ten in Yājñavalkya Smṛti, where 105 and 107 named lakṣa and koṭi, respectively.
Classical antiquity
In the Western world, specific
In The Sand Reckoner, Archimedes (c. 287–212 BC) devised a system of naming large numbers reaching up to
- ,
essentially by naming powers of a myriad myriad. This largest number appears because it equals a myriad myriad to the 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 at this number because he did not devise any new
Archimedes' goal was presumably to name large powers of 10 in order to give rough estimates, but shortly thereafter, Apollonius of Perga invented a more practical system of naming large numbers which were not powers of 10, based on naming powers of a myriad, for example, would be a myriad squared.
Much later, but still in antiquity, the Hellenistic mathematician Diophantus (3rd century) used a similar notation to represent large numbers.
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 '
Modern use of large finite numbers
Far larger finite numbers than any of these occur in modern mathematics. For instance,
Infinity
The ultimate in large numbers was, until recently, the concept of infinity, a number defined by being greater than any finite number, and used in the mathematical theory of limits.
However, since the 19th century, mathematicians have studied
References
- ^ Yajurveda Saṁhitâ, xvii. 2.
- ^ 無量大数の彼方へ
- ^ 大数の名前について
- ISBN 978-0-19-875523-4. Archivedfrom the original on April 3, 2017.
- ^ "CH. Rayo's Number". The Math Factor Podcast. Retrieved 24 March 2014.