Let \(T\) consist of all integers larger than or equal to \(a\) which are not in \(S.\) The theorem will be proved if \(T=\emptyset .\) If \(T\neq \emptyset\) then by the well ordering principle, ther...Let \(T\) consist of all integers larger than or equal to \(a\) which are not in \(S.\) The theorem will be proved if \(T=\emptyset .\) If \(T\neq \emptyset\) then by the well ordering principle, there would have to exist a smallest element of \(T,\) denoted as \(b.\) It must be the case that \(b>a\) since by definition, \(a\notin T.\) Thus \(b\geq a+1\), and so \(b-1\geq a\) and \(b-1\notin S\) because if \(b-1\in\) \(S,\) then \(b-1+1=b\in S\) by the assumed property of \(S.\) Therefore, \(b-…
