First-Order Logic

This book is about a formal approach to mathematical structures. Formal methods are by their very nature formal. When studying mathematical logic, initially one often has to grit ones teeth and absorb certain preliminary definitions on faith. Concepts are given precise definitions, and their meaning is revealed later, after one has had a chance to see their utility. We will try to follow a different route. Before all formalities are introduced, in this chapter, we will take a detour to see examples of mathematical statements and some elements of the language that is used to express them.