‘Excellent!’ I cried. ‘Elementary,’ said he.
by Arthur Conan Doyle (1859–1930)
To communicate, we sometimes need to agree on the meaning of certain terms. If the same idea is mentioned several times in a discussion, we often replace it with some shorthand notation. The choice of notation can help us avoid wordiness and ambiguity, and it can help us achieve conciseness and clarity in our written and oral expression.
Since much of our communication involves reasoning about things, we’ll begin this chapter with a discussion about the notions of informal proof. The rest of the chapter is devoted to introducing the basic notions and notations for sets, ordered structures, graphs, ...