Lesson 1

As we have seen, to prove that an object with the desired properties exists, it is enough to simply present such an object. And for this to be considered a rigorous mathematical proof of existence, it is not even necessary to explain how exactly this object was found or constructed.

But how do we prove that an object with the desired properties does not exist? There is no general recipe for this. The desired object may not exist for a variety of reasons. This can even manifest within a single problem. Let's give an example.