07.4 Constructive Proofs
7.4 Constructive Proofs A constructive proof proves existence by producing an object. It does not merely show that failure is impossible. It gives a witness, an algorithm, or a method that builds the required object. The basic form is: $$ \exists x \in X,\ P(x). $$ A constructive proof supplies a specific $x$ and verifies that $P(x)$ holds. For example, to prove that there exists an even prime number, we...