Nonconstructive Proof/Examples

Examples of Nonconstructive Proofs

Natural Number

This is the shape of a proof which is nonconstructive:

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.