History of Hindu Mathematics: A Source Book v1.c8.s15.2

v1.c8.s15.2

**Zero in Arithmetic.** The Hindus in their arithmetic define zero as the result of the operation $a - a = 0$ This definition is found in Brahmagupta's work¹ and is repeated in all later works. It is directly used in the operation of subtraction. In carrying out arithmetical operations, the results of the operations of addition, subtraction and multiplication of zero and by zero are required. The Hindus did not recognise the operation of division by zero as valid in arithmetic; but the division of zero by a number was recognised as valid. Nârâyaṇa in his *pâṭîgaṇita* (arithmetic) has clearly stated this distinction: