The first attempt to define the division by zero was done by Brahmagupta around 628 CE. After that, Bhaskaracarya (c. 1150), while discussing the mathematics of zero in Bijaganita, explains that infinity (ananta-rasi) which results when some number is divided by zero is called khahara. He also mentions the characteristic property of infinity that it is unaltered even if many are added to or taken away from it.
The verse that discuss this is:
This verse translates to:
A quantity divided by zero will be called khahara (an entity with zero as divisor).
Tell me . . . three divided by zero . . . This infinite (ananta or that without end) quantity 3/0 is called khahara.
In this quantity, khahara, there is no alteration even if many are added or taken out, just as at the period of destruction or creation of the worlds, though numerous orders of beings are absorbed or put forth.
Reference: Bijaganita by Bhaskaracarya