How did Brahmagupta define arithmetic rules for zero?

In his seminal work Brahma-sphuta-siddhanta (628 CE), the Indian mathematician Brahmagupta became the first scholar to treat zero—referred to as shunya—as a number in its own right rather than merely a placeholder.12

Brahmagupta defined zero as the result obtained when a number is subtracted from itself. Building on this, he established foundational arithmetic rules for operations involving zero, as well as for positive numbers (which he termed "property") and negative numbers (which he termed "debts").12

While his work provided the essential framework for zero as a number, it is important to note that modern mathematics maintains that division by zero remains undefined, as no real number multiplied by zero can produce a nonzero result. Brahmagupta’s contributions were instrumental in the development of Indian mathematics and eventually influenced the global adoption of the Hindu-Arabic numerals through their transmission to the Islamic world and later to Europe.21