15-317 Constructive Logic
Recitation 1: Clue

We used a little logic problem based on the game Clue to explore some basic concepts: translating logical statements from natural language into mathematical notation, and proving theorems using rules of inference.

To illustrate a difference between constructive and classical proofs, we also looked at a proof of the following statement: for any natural number x, either there exists a natural number y such that x = 2*y or there does not exist a natural number y such that x = 2*y. Constructively, we can prove this using the Division Theorem and it yields an evenness-testing algorithm. Classically, the proof is trivial and gives us no information.

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Frank Pfenning