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.