Non-constructive Proofs

A non-constructive proof shows that something exists without actually providing a specific example or method to find it. It typically relies on logical arguments, such as contradiction or counting, to conclude that an object must exist. For example, it might prove that there is a solution to a problem by showing that assuming no solution leads to a contradiction, rather than explicitly constructing the solution itself. This approach is valued in mathematics because it establishes existence logically, even when finding or describing the object directly might be difficult or unknown.