

Mathematical Reasoning: Writing and Proof is designed to be a text for the &filig;rst course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics.

• ## 3: Constructing and Writing Proofs in Mathematics

A proof in mathematics is a convincing argument that some mathematical statement is true. A proof should contain enough mathematical detail to be convincing to the person(s) to whom the proof is addressed. In essence, a proof is an argument that communicates a mathematical truth to another person (who has the appropriate mathematical background). A proof must use correct, logical reasoning and be based on previously established results.
• ## 4: Mathematical Induction

Mathematical induction is a mathematical proof technique that is used to prove that a property P(n) holds for every natural number n, i.e. for n = 0, 1, 2, 3, and so on.