ABSTRACT
In the previous chapter the distinction was made between a sample and a population. A central problem for statisticians is that of devising ways of thinking which guard against ‘jumping to conclusions’ and attributing to a whole population what has been found out about a sample, without a scientific word of caution about the confidence you can legitimately have in such conclusions. In many respects, this is also a central, and much neglected, concern within mathematics. Remember the definitions of the universal and existential quantifiers in Chapter 4, Section 5. Their use is in emphasising the difference between cases of something being true for all possibilities and something being true for just some possibilities. In this chapter the notion and strategies of proof will be explored. The appreciation of what is involved in designing your own proofs and following the proofs of others will, it is hoped, be enhanced by contrasting proof with strategies of provision of partial evidence for generalisations. The citing of particular examples, the use of diagrams to support general arguments, the contrast between deduction and induction and the process of searching for exceptions to either disprove a generalisation or impose a limitation on it will provide the backdrop to the presentation of mathematical proof.
