Abstract
A mathematical proof is an inferential argument for a mathematical statement showing that the stated assumptions methodically and logically lead to guarantee the conclusion. The focus of this chapter is on proof methods, noting that every statement that is not an axiom or definition needs to be proven. The proof methods discussed are proofs of equivalence, proofs by counterexample, vacuous proofs, trivial proofs, direct proofs, proofs by contraposition, proofs by contradiction, proof by cases, proofs by exhaustion, constructive proofs, nonconstructive proofs, proof of a disjunction, and uniqueness proofs. Note that each type of proof is accompanied by a variety of examples.
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