Proofs

There are statements that have not and perhaps cannot be proved. Data can be displayed and patterns can be anticipated but a proof requires a logical process. Statistics can be used to establish a link between events but often the reliability factor is established at only 95%. Accounting firms will retest a hypothesis using a larger sample if the initial hypothesis test fails. Even then two types of errors exist for each hypothesis: rejecting it by mistake and incorrectly accepting it. It is similar to `reasonable doubt' although some will believe the statistical claims (at least until another study is released). Any statement can be proved false by one counter example. A correct example though only illustrates there may be a possible proof. In this book you will explore common methods of mathematical proof using various topics. Consider it as a supplement to a text.