I think it's a matter of convention, and that all the maths I can think of survives the following definitions:
If infinity were to be defined as immeasurably large, and zero as immeasurably small, we would be saying infinity=(some finite number)/0 and 0=(some finite number/infinity
This still leaves us unable to find an definite answer to the multiplication of 0 and infinity, because we might have chosen any 2 finite numbers for the definitions above.
If infinity were to be defined as immeasurably large, and zero as immeasurably small, we would be saying infinity=(some finite number)/0 and 0=(some finite number/infinity
This still leaves us unable to find an definite answer to the multiplication of 0 and infinity, because we might have chosen any 2 finite numbers for the definitions above.