Alternative proofs of some results from elementary analysis (Q1407447)

The authors, in an ``endeavor to encourage mathematics students to search for and study various methods of proof'', offer alternative proofs for several theorems of elementary analysis, including the following: Theorem 1: A real-valued function which is 1-1 and continuous on an interval \(I\) in the reals is either increasing or decreasing on \(I\). Dini's lemma. The Bolzano-Weierstrass theorem. The Heine-Borel theorem. The Cauchy-Schwarz inequality for complex numbers. The Lagrange identity for complex numbers.