Definition:Constructive Proof

Definition

A constructive proof is a proof in which there exists an effective procedure for the construction of every object in it.

Examples

Nonconstructive Proof

By way of illustration, this is the shape of a proof which is not constructive:

It is false that every number $n$ lacks the property $P$.

Therefore there exists at least one number $n_0$ that has property $P$.

Unless an example of such a $n_0$ can be constructed, such an argument is not allowed in a constructive proof.

Also see

• Definition:Constructive Definition
• Definition:Intuitionism

• Definition:Nonconstructive Proof

• Results about constructive proofs can be found here.

Sources

• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): constructive