Editing Mathematical proof (section)

===Proof by construction===
{{Main|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 number]]s by constructing an [[Liouville number|explicit example]].  It can also be used to construct a [[counterexample]] to disprove a proposition that all elements have a certain property.