I think this is only because you don't care dividing by zero. But you may as well define the value at zero to be 0, and any other value at least 1. See this expository paper by Keith Conrad for interesting remmarks on euclidean domains and functions.

I think this is only because you don't care dividing by zero. But you may as well define the value at zero to be 0, and any other value at least 1. See this expository paper by Keith Conrad for interesting remarks on euclidean domains and functions.