[marcosdumay]

> There are multiple extensions to the real numbers that allow division by zero.

Well, the gotcha is that they redefine the operations so that none of addition, subtraction, multiplication or division are total. Those operations just break in a different number than zero.

[nextaccountic]

Addition can be total if you have a single infinity, just make infinity + n = infinity for all n

Subtraction, multiplication and division is harder

But making further operations partial isn't that of a big deal; in fields the division is already partial due to division by zero not being defined.