Definition:Non-Constructive Proof

Definition

A non-constructive proof is a proof in which there does not exist an effective procedure for the construction of every object in it.

That is, such that it requires an infinite number of steps to complete.

Examples

Natural Number

This is the shape of a proof which is non-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 Proof
• Definition:Intuitionism

• Results about non-constructive proofs can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): intuitionism
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): intuitionism