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Chapter 1 Logic and Proofs
Contrariwise, if it was so, it might be; and if it were so, it would be; but as it isn’t, it ain’t. That’s logic.
―Lewis Carroll (1832--1898)
In this chapter, we discuss logic and proofs. The rules of logic specify the meaning of mathematical statements. These rules help us understand and reason with these statements to construct arguments to justify the truth of certain statements. Once we prove a mathematical statement true, we call it a
theorem . The argument of justification is called a
proof .
Clear reasoning and communication of ideas are important in all disciplines. We restrict ourselves to a small, but important corner of mathematics where we can completely describe the theory with minimal prerequisites. The skills you gain are applicable to many other situations.
