Why are some arguments convincing while others are not? What makes an argument convincing? How can you establish your argument in such a way that no room for doubt is left? How can mathematical thinking help us deal with this? In this chapter, we will start by digging into these questions. Our goal here is to learn by examples how to understand proofs, how to discover them on your own, how to explain them, and — last but not least — how to enjoy them: we will see how a small remark or a simple observation can turn a seemingly non-trivial question into one with an obvious answer.
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