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History of large numbers

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 that did not get further than ten thousand, even if there were systems that allowed to write huge numbers, used only as a matter of philosophical speculation, like the one devised by Archimedes that could have reached 10800,000,000, but was actually used only up to 1064. The Romans 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 .

However, the Indians, who also invented the positional number system and the zero, were much more advanced in this aspect than all the other civilisations of Antiquity and the Middle Ages. By the 7th century AD Indian mathematicians were familiar enough with the notion of infinity as to define it as the quantity whose denominator is zero.

This achievement can probably be explained by the Indians' passion for high numbers, which is intimately related to their religious thought. For example, in texts belonging to the Vedic literature which are dated around the third century AD we find individual Sanskrit names for each of the powers of 10 up to 1012. (Even today, the words 'lakh' and 'koti', referring to 100,000 and 10,000,000, respectively, are in common use among English-speaking Indians.)

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.

It is interesting to note that there is also an analogous system of Sanskrit terms for fractional numbers, which shows the capacity to deal with both very high and very small numbers.

Reference: Georges Ifrah, The Universal History of Numbers, ISBN 186046324X

One interresting point in using large numbers is the confusion on the term Billion and Milliard in many countries.



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