First you'd need that the integers are an integral domain and then build up to the fact that the reals are a field. At least that's how I'd go about it. Maybe

First you'd need that the integers are an integral domain and then build up to the fact that the reals are a field. At least that's how I'd go about it. Maybe one can start with the reals themselves. Here's the proof that the integers have no zero divisors: https://proofwiki.org/wiki/Ring_of_Integers_has_no_Zero_Divisors https://proofwiki.org/wiki/Ring_of_Integers_has_no_Zero_Divi...