What do the statements 2 + 2 = 4 and "the sky is blue" have in common? One might say that they are both true. The statement about the sky can be confirmed by going outside and observing the color of the sky. How, then, can one confirm the...

A proof is a logical argument demonstrating that a specific statement, proposition, or mathematical formula is true. It consists of a set of assumptions, or premises, which are combined according to logical rules, to establish a valid conclusion. This...

In mathematics, a proof is a demonstration that, assuming certain axioms and rules of inference, some statement is necessarily true. A proof is a logical argument, not an empirical one. That is, one must demonstrate that a proposition is true in all...

MATHEMATICAL REASONING: WRITING AND PROOF by Ted Sundstrom Prentice-Hall, Upper Saddle River, NJ, 2003, 435 pp. If it is true that "mathematics is proof, as teachers often tell their students, then this book is an excellent beginning to the learning of mathematics. Of...

JOURNEY INTO MATHEMATICS: AN INTRODUCTION TO PROOFS by Joseph Rotman Prentice-Hall, Englewood Cliffs, NJ, 237 pp., 1999 THE MOMENT OF PROOF: MATHEMATICAL EPIPHANIES by Donald C. Benson Oxford University Press, New York, NY, 331 pp., 1999 These are two delightful...