Formal knowledge
Constructive mathematics
Mathematics that requires explicit constructions or evidence for existence claims.
Definition
Constructive mathematics
Constructive mathematics avoids some classical principles and treats a proof of existence as a method for constructing a witness.
A constructive proof of P or not P must determine which side holds. A constructive existence proof must provide enough information to obtain the object.
01
Example
To prove that an integer with property P exists, a constructive proof supplies an integer and evidence that it has P.
02
Important distinction
Constructive does not mean computationally fast, and classical does not mean invalid.
After reading this article, you should be able to
- Define Constructive mathematics in the sense used on this site.
- Distinguish constructive evidence for existence from a proof by contradiction that provides no witness.