structural:expansion, quality:corruption
Early attempts

The Brāhmasphuṭasiddhānta of Brahmagupta (c. 598–668) is the earliest text to treat zero as a number in its own right and to define operations involving zero. According to Brahmagupta,

A positive or negative number when divided by zero is a fraction with the zero as denominator. Zero divided by a negative or positive number is either zero or is expressed as a fraction with zero as numerator and the finite quantity as denominator. Zero divided by zero is zero.

In 830, Mahāvīra unsuccessfully tried to correct the mistake Brahmagupta made in his book Ganita Sara Samgraha: "A number remains unchanged when divided by zero."

Bhāskara II 's Līlāvatī (12th century) proposed that division by zero results in an infinite quantity,

A quantity divided by zero becomes a fraction the denominator of which is zero. This fraction is termed an infinite quantity. In this quantity consisting of that which has zero for its divisor, there is no alteration, though many may be inserted or extracted; as no change takes place in the infinite and immutable God when worlds are created or destroyed, though numerous orders of beings are absorbed or put forth.

Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to a 0 {\textstyle {\tfrac {a}{0}}} is contained in Anglo-Irish philosopher George Berkeley 's criticism of infinitesimal calculus in 1734 in The Analyst ("ghosts of departed quantities").