Algebra: Abstract and Modern

2

Number Systems

2.1 Integers

2.2 Congruence Modulo n

2.3 Rational, Real and Complex Numbers

2.4 Ordering

2.5 Matrices

2.6 Determinants

This chapter is meant to review some of the important properties of the set of positive integers, the set of integers, the set of rational numbers, the set of real numbers and the set of complex numbers. We do not discuss any axiomatic development of these systems. We simply assume familiarity with addition and multiplication of these and their usual properties. Also, we briefly discuss the concept of a partial order on a set in general and the usual ordering on the real number system, in particular, these facilitate us in facing several encounters with these throughout this book. Further, we recall the notion ...