Logic and proofs

Abstract

We formulate mathematical arguments in our natural language. But our everyday language is often ambiguous, and quite often you hear logical fallacies. Therefore, if you want to argue reliably then you should know well both the basic logical structures and the phrases we use to express them. In the course of a mathematical investigation you make observations, discover patterns, have insights, make conjectures. In order to be sure that a conjecture is true you need a proof.