We begin our journey by taking a closer look at some familiar notions, such as quadratic equations and inequalities. And, rather than using mechanical computations and algorithms, we focus on more fundamental questions: Where does the quadratic formula come from and how can we prove it? What are the rules that can be used with inequalities, and how can we justify them? These questions will lead us to looking at a few proofs and mathematical arguments. We highlight some of the main features of a mathematical proof, and discuss the process of constructing mathematical proofs. We also review informally the types of numbers often used in mathematics and introduce relevant terminology.
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