Priscilla Dufweke-Lantto: Constructing the Mean Value Theorem

Abstract.

This thesis explores the foundational framework of constructive analysis, replacing classical nonconstructive principles such as The Law of Excluded Middle (LEM) with explicit constructive methods that culminate in a proof of the Mean Value Theorem. By strengthening notions of continuity and carefully refining foundational concepts, it shows how classical results can be reestablished by discarding assumptions that fail to produce explicit constructive examples.