In the proof of √2, which option correctly distinguishes an ordinary rational form from the proof-ready form?

Correct answer: In the proof, a/b should be taken in lowest form with gcd(a,b)=1

Every rational number can be written as a/b with integer a and non-zero integer b, but the irrationality proof needs a special, reduced representation. We choose a/b in lowest terms, expressed by gcd(a,b)=1. Assuming √2=a/b then gives a²=2b². The parity argument forces a and b both to be even, which contradicts the reduced-form condition because they would share the factor 2. Thus option A states the proof-ready form precisely. A zero denominator is not allowed in a fraction, and requiring both entries to be even would destroy the contradiction rather than create it. Equal numerator and denominator is also irrelevant and would describe only a restricted fraction, not every rational number.