LARGE & SMALL NUMBERS IN ANCIENT INDIA

Ancient Indians were the first who invented zero and decimal place value system during Rigvedic period. The scientific naming system of numerals in Vedic Sanskrit indicates that decimal place value system was well established. The compounded words for numerals like Ekadasa (Eka+dasa) = one and ten, Ekavimshati (Eka+vimshati) = one and twenty, Ekatrimshat (Eka + trimshat) = one and thirty etc. indicate that Eka will be always the first word and Dasa will be always second word which implies the position of a number is most important since the symbol of unit & the symbol of ten cannot interchange their positions without affecting the value of the numbers. Thus units must be counted first later tens and so on. The use of large numbers up to 10^12 considering the powers of 10 in Yajurveda was also not possible without having the knowledge of place value system and zero.

Ramayana gives the counting of large numbers from 10 to the power of 7 to 10 to the power of 62.
Koti = 100000 x 100 = 10^7
Shanku = Koti x 1000 x 100 = 10^12
Mahashanku = Shanku x 1000 x 100 = 10^17
Vrinda = Mahashanku x 1000 x 100 = 10^22
Mahavrinda = Vrinda x 1000 x 100 = 10^27
Padma = Mahavrinda x 1000 x 100 = 10^32
Mahapadma = Padma x 1000 x100 = 10^37
Kharva = Mahapadma x 1000 x 100 = 10^42
Mahakharva = Kharva x 1000 x 100 = 10^47
Samudra = Mahakharva x 1000 x 100 = 10^52
Mogha = Samudra x 1000 x 100 = 10^57
Mahaugha = Mogha x 1000 x100 = 10^62

Mahabharata also used large numbers up to 10^52.
Lalitavistara is a biography of Buddha and belong to Mahayana school of Buddhism written around 100 AD. Lalitavistara gives the evidence of use of infinitely large and small numbers.
According to the story of Lalitavistara, A svayamvara (competition for marriage) was organized for Princess Gopa in which Prince Siddhrtha participated. Apart from other competitions like horse riding, archery etc., Siddhartha had to undergo the test of mathematics.
Arjuna a great mathematician asked Siddhartha "Do you know the procedure of Kotishatottara (counting after hundred crores)". Explaining the procedure of Kotishatottara,Siddhartha counted large numbers starting from Koti (10^7), calculating in multiples of 100 up to Tallakshana (10^53) referring as first numeration.
Koti x 100 = Ayuta (10^9)
Ayuta x 100 = Niyuta (10^11)
Niyuta x 100 = Kankara (10^13)
Kankara x 100 = Vivara (10^15)
Vivara x 100 = Akshobhya (10^17)
Akshobhya x 100 = Vivaha (10^19)
Vivaha x 100 = Utsanga (10^21)
Utsanga x 100 = Bahula (10^23)
Bahula x 100 = Nagabala (10^25)
Nagabala x 100 = Titila (10^27)
Titila x 100 = Vyavasthanaprajnapti (10^29)
Vyavasthanaprajnapti x 100 = Hetuhila (10^31)
Hetuhila x 100 = Karahu (10^33)
Karahu x 100 = Hetvindriya (10^35)
Hetvindriya x 100 = Samaptalambha (10^37)
Samaptalambha x 100 = Gaganagati (10^39)
Gaganagati x 100 = Niravaravadya (10^41)
Niravaravadya x 100 = Mudrabala (10^43)
Mudrabala x 100 = Sarvabala (10^45)
Sarvabala x 100 = Visangyagati (10^47)
Visangyagati x 100 = Sarvasangya (10^49)
Sarvasangya x 100 = Vibhutangama (10^51)
Vibhutangama x 100 = Tallakshana (10^53)

Building on this first numeration, next eight numerations also have 23 multiplicative steps of 100 and the last number expressed by Siddhartha was 10^421(Uttaraparamanurajahpravesha).

Again replying to Arjuna, Siddhartha talked about "Paranamu"(subtle atoms) with bottom up approach and particles composed of atoms.
Paramanu (subtle atom) x 7 = Renu (fine particle)
Renu x 7 = Truti (small particle)
Truti x 7 = Vatayanarajah
Vatayanarajah x 7 = shasharajah
shasharajah x 7 = Edhakarajah
Edhakarajah x 7 = Gorajah
Gorajah X 7 = Liksharajah
Liksharajah x 7 = sarshapa
sarshapa x 7 = Yava (breadth of barley)
Yava x 7 = Anguli
Anguli x 12 = Vitasti
Vitasti x 2 = Hasta (cubit)
Hasta x 4 = Dhanu
Dhanu x 1000 = Krosha
Krosha x 4 = Yojana

Assuming an Anguli = finger is 4 centimetres long, the "Paramanu"(subtle atom) is therefore, 4 centimetres divided by 7 ten times, which is 0.04 meter x 7 to the minus 10 or 0.00000000001416 meter (70 trillionths of a meter), which comes amazingly close to the actual size of carbon atom.

After discussing infinitely large and small numbers, Siddhartha accepted the challenge to calculate the mass of one Yojana. Siddhartha calculated the mass of one Yojana as 10003000000000000060320512000 atoms. According to Buddhist cosmology, there are three thousand crore worlds in the universe each measuring 34000 yojanas. The question arises how many atoms are there in the universe. Siddhartha replied that there are Asamkhyata (innumerable) atoms in the universe. When 7 paramanus combine each other then only paramanus occupy space but there are innumerable paramanus in the world do not combine each other, thus, do not occupy space. Therefore, in view of Siddhartha, paramanus in the universe are innumerable. In the modern theory of quantum-mechanics, quarks enter into existence and disappear all the time in the vacuum. Therefore the quantum information is not fixed or innumerable.

What a glorious heritage!!!! Lalitavistara was translated into Chinese during 2nd century. Therefore, Lalitavistara cannot be dated later than 1st century. Possibly, it might have written few hundreds years before 2nd century. Unfortunately, Modern textbooks teach us that Aryabhata invented zero in 5th century and Indians had no knowledge of zero and place value system before 5th century. Interestingly, one grant of Katachchuri king Taralswami is dated in the year 346 and the year is recorded in decimal place value notation. Historians declared this grant as forgery because Indians had no knowledge of plave value system before 5th century. Shame on these historians.

Evidently, Indians had the knowledge of zero and place value system since Vedic period. Racist western and Eurocentric scholars do not accept this fact. Therefore, we teach our children that Indians had no knowledge of Zero and place value system before 5th century.