Try It on a Classic

Work through a small proof by contradiction in your own words. Claim: there is no largest even number.

Assume the opposite: there is a largest even number N. Consider N + 2. It is even. And N + 2 is larger than N. But we said N was the largest — contradiction. The assumption was wrong.

Try a harder one: there is no smallest positive rational number. Suppose the opposite — call it r. Then r/2 is also positive and smaller than r. Contradiction again.

After five reps of this drill, you start seeing the move in everyday arguments: if your conclusion leads to something absurd, your starting point needs checking.