Chapter 2

Proofs, Induction, and Number Theory

Proof techniques
We are doing simpler proofs than the ones in Predicate logic

General form of most proofs is (∀x)(Px→Qx)

Proof of square root of 2 being irrational
 * Proof by contradiction
 * find a contradicting answer
 * Proof by exhaustion
 * exhaust all possible cases to prove it is the case
 * Proof by contraposition
 * assume what you want to prove is false
 * prove this is a contradiction

1st principle of mathematical induction
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2nd principle of mathematical induction
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