Note on the Inequality Theorem that mx^m–1(x – 1)>x^m – 1>m(x – 1) unless when 0<m<1, when mx^m–1(x – 1)<x^m – 1<m(x – 1), where x is any positive quantity other than unity

Extract

The proof given in Chrystal's Algebra, II., pp. 42–5, of this very important theorem is deduced from elementary algebraical principles : and, though somewhat involved, is of great value, as it establishes what must be considered a fundamental theorem in the Calculus.