nonconstructively
Nonconstructively is an adverb used to describe proofs, arguments, or methods that establish the existence of an object without providing a specific example or explicit procedure to obtain it. In mathematics, nonconstructive reasoning is common in classical contexts, where the law of the excluded middle and, in many cases, the axiom of choice may be invoked. A nonconstructive proof may show that an object with a given property must exist by arguing that assuming otherwise leads to a contradiction, or by appealing to a counting or density argument that guarantees existence without exhibiting a witnessing instance.
Typical examples involve existence results that do not yield a concrete example. For instance, the existence
Impact and context: nonconstructive proofs can deliver broad existence results with relatively little computational content. They