Constructive Proof/Examples/Non-Constructive Proof

Example of Non-Constructive 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.

Sources

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