how was zero used before its discovery by Aaryabhatta
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I think we can count indefinitely without ever using 0. 0 is a symbol, a convenience and a convention, not a mathematical priori. That's precisely the reason why it is called an invention and not a discovery.
How many times do you utter the word "zero" while counting till hundred ? Not once, right ?.
Zero is "applied" in decimal number system because it makes conducting mathematical operations incredibly easy, which other systems couldn't guarantee us.
Vedas, that were written much before Aryabhatta have verses like :
dvâdaśa pradháyaś cakrám ékaṃ, trîṇi nábhyāni ká u tác ciketa tásmin sākáṃ triśatâ ná śaṅkávo, 'rpitâḥ ṣaṣṭír ná calācalâsaḥ.
Here Dvadasa means 12, Sakam means Sixty, Trisata means Three Hundred, hence Sakam Trishata means 360.
As evident, we don't need 0 for writing/speaking 60, 300.
So, Sahasraarjun has 1000 hands, Shat Kauravas are 100 Kauravas and Dashanan is Ravana with 10 heads.
The idea of a zero-less counting system seems impossible to us because we deal with it on a daily basis and we rarely use any other system of counting.
Speaking mathematically, even the concept of zero varies with the context. You can conceive it as absence of numbers, or a neutral on an integral line, or as a source/origin in a multi-dimensional space.
In my opinion, zero was always known to ancient Vedic Indians. Not only Ravana and Kauravas, you can find several references to 1000, lakh and crore in our texts. For example please read the following chapter from Bhagavatam which defines time from Nano second to several yugas (SB 3.11: Calculation of Time, from the Atom). Surely, this wouldn't have been possible without the knowledge of zero.
I would say Aryabhatta defined the formal definition of place value using Zero and its mathematical usage, because his work was intended to be a Mathematical treatise. Our Puranas and Itihasas on other hand were not Mathematical texts - Maths in them were incidental.
How many times do you utter the word "zero" while counting till hundred ? Not once, right ?.
Zero is "applied" in decimal number system because it makes conducting mathematical operations incredibly easy, which other systems couldn't guarantee us.
Vedas, that were written much before Aryabhatta have verses like :
dvâdaśa pradháyaś cakrám ékaṃ, trîṇi nábhyāni ká u tác ciketa tásmin sākáṃ triśatâ ná śaṅkávo, 'rpitâḥ ṣaṣṭír ná calācalâsaḥ.
Here Dvadasa means 12, Sakam means Sixty, Trisata means Three Hundred, hence Sakam Trishata means 360.
As evident, we don't need 0 for writing/speaking 60, 300.
So, Sahasraarjun has 1000 hands, Shat Kauravas are 100 Kauravas and Dashanan is Ravana with 10 heads.
The idea of a zero-less counting system seems impossible to us because we deal with it on a daily basis and we rarely use any other system of counting.
Speaking mathematically, even the concept of zero varies with the context. You can conceive it as absence of numbers, or a neutral on an integral line, or as a source/origin in a multi-dimensional space.
In my opinion, zero was always known to ancient Vedic Indians. Not only Ravana and Kauravas, you can find several references to 1000, lakh and crore in our texts. For example please read the following chapter from Bhagavatam which defines time from Nano second to several yugas (SB 3.11: Calculation of Time, from the Atom). Surely, this wouldn't have been possible without the knowledge of zero.
I would say Aryabhatta defined the formal definition of place value using Zero and its mathematical usage, because his work was intended to be a Mathematical treatise. Our Puranas and Itihasas on other hand were not Mathematical texts - Maths in them were incidental.
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