Different cultures used different traditional numeral systems for naming large numbers. The extent of large numbers used varied in each culture. Two interesting points in using large numbers are 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.
The Indians had a passion for high numbers. 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. One of these Vedic texts, the Yajur Veda, even discusses the concept of numeric infinity, stating that if you subtract purna from purna, you are still left with purna. The Lalitavistara Sutra 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 nirabhilapya nirabhilapya parivarta or 1037218383881977644441306597687849648128, which appeared as Bodhisattva's maths in the Avataṃsaka Sūtra., though chapter 30 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 104*5*2121 and continuing a similar expansion indeterminately. A few large numbers used in India by about 5th century BC :
In the Western world, specific number names for 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. In The Sand Reckoner, Archimedes 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 ordinal numbers to match his new cardinal numbers. Archimedes only used his system up to 1064. 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, Much later, but still in antiquity, the Hellenistic mathematicianDiophantus 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 word 'million' was introduced.
Far larger finite numbers than any of these occur in modern mathematics. For instance, Graham's number is too large to express using exponentiation or even tetration. For more about modern usage for large numbers, see Large numbers. To handle these numbers, new notations are created and used.
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 transfinite numbers, 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 cardinals. The concept of transfinite numbers, however, was first considered by Indian Jaina mathematicians as far back as 400 BC.
