Zero is strangest number in the universe and continuing its role as one of the great paradoxes of human thought. It is both nothing and everything.
Zero is an even number, because it is divisible by 2. By most definitions 0 is a natural number, and then the only natural number not to be positive. The number 0 is the smallest non-negative integer.
The number 0 is neither positive nor negative and appears in the middle of number line. It is neither a prime number nor a composite number. It cannot be prime because it has an infinite number of factors and cannot be composite because it cannot be expressed by multiplying prime numbers (0 must always be one of the factors).
Initially, the zero as a number was not available. There was the idea of empty space, which may be thought conceptually similar to zero. Babylonians around 700 BC used three hooks to denote an empty place in the positional notation.
Almost during the same time, Greek mathematicians made some unique contributions to mathematics. Euclid wrote a book on number theory named Elements, but that was completely based on geometry and no concept of zero was mentioned.
Around AD 650, the use of zero as a number came into Indian mathematics. The Indians used a place-value system and zero was used to denote an empty place. In fact there is evidence of an empty placeholder in positional numbers from as early as 200AD in India. Around 500 AD Aryabhata devised a number system, which had no zero, as a positional system, but used to denote empty space. There is evidence that a dot had been used in earlier Indian manuscripts to denote an empty place in positional notation. For example, to represent ‘100’ it would be two dots after 1.
In 628 AD, Brahmagupta wrote Brahmasphutasiddhanta (The Opening of the Universe), and attempted to give the rules for arithmetic involving zero and negative numbers. He explained that given a number, if you subtract it from itself you obtain a zero. He gave the following rules for addition, which involve zero: The sum of zero and a negative number is negative, the sum of a positive number and zero is positive; the sum of zero and zero is zero. Similarly, he gave the correct rules for subtraction also. But when it comes to division by zero, he gave some rules that were not correct.
In 830, Mahavira wrote Ganita Sara Samgraha (Collections of Mathematics Briefings), which was designed as an update of Brahmagupta’s book. He correctly stated the multiplication rules for zero, but again gave incorrect rule for division by zero.
After 500 years of Brahmagupta, Bhaskara tried to solve the problem of division by stating that any number divided by zero was infinity. Well, conceptually though it is still incorrect (division by zero is indeterminate not infinity), Bhaskara did correctly state other properties of zero, such as square of zero is zero and square root of zero is also zero.
The Islamic and Arabic mathematicians took the ideas of the Indian mathematicians to further west.
Source: Organiser
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