In the first chapter we were mainly interested in the meaning of mathematical statements. However, mathematics is primarily concerned with establishing the truth of statements. This is achieved by giving a proof of the statement, The key idea in most proofs is that of implication and this idea is discussed in this chapter.
A proof is essentially a sequence of statements starting from statements we know† to be true and finishing with the statement to be proved. Each statement is true because the earlier statements are true. The justification for such steps usually makes use of the idea of ‘implication’; an implication is the assertion that if one particular statement is true then another particular statement is ...