Constructive proof

method of proof that demonstrates the existence of a mathematical object by creating or providing a method for creating the object

In mathematics, a constructive proof is a method of proof that shows the existence of a mathematical object—by giving a method on how to create the object. The other type of proof is called non-constructive proof, or existence proof: It shows that an object must exist, but does not give a way how to construct it.[1][2][3]

A non-constructive proof is rejected by the so-called constructivists, who choose to interpret existence in a stricter way.[1]

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ReferencesEdit

  1. 1.0 1.1 "The Definitive Glossary of Higher Mathematical Jargon: Constructive Proof". Math Vault. 2019-08-01. Retrieved 2020-09-23.
  2. "7.4: Constructive Versus Non-Constructive Proofs". Mathematics LibreTexts. 2019-10-18. Retrieved 2020-09-23.
  3. "Constructive Versus Existential Proofs". zimmer.csufresno.edu. Retrieved 2020-09-23.