Proofs
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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 ...
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.
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