The mathematics teacher has from time to time to make a decision as to how much he should say to a class about a topic which is too difficult to discuss with full mathematical rigour. This situation may arise with students who are too young or too immature in their mathematical development to appreciate a rigorous discussion, or with older students who are interested in mathematics purely as a tool which they require in the study of other subjects such as engineering and have not time to spare even if they would be interested in a rigorous development of the particular topic.