15317 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
evennesstesting algorithm. Classically, the proof is trivial and
gives us no information.
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Frank Pfenning
