section_path: Methods of proof/Proof by construction
section_name: Proof by construction
paragraph_text: Proof by construction
  
  Proof by construction, or proof by example, is the construction of a concrete example with a property to show that something having that property exists. Joseph Liouville, for instance, proved the existence of transcendental numbers by constructing an explicit example. It can also be used to construct a counterexample to disprove a proposition that all elements have a certain property.