Table of Contents

Natural Numbers:; 1.1 Axioms; 1.2 Addition; 1.3 Ordering; 1.4 Multiplication Fractions:; 2.1 Definition and equivalence; 2.2 Ordering; 2.3 Addition; 2.4 Multiplication; 2.5 Rational numbers and integers Cuts:; 3.1 Definition; 3.2 Ordering; 3.3 Addition; 3.4 Multiplication; 3.5 Rational cuts and integral cuts Real Numbers:; 4.1 Definition; 4.2 Ordering; 4.3 Addition; 4.4 Multiplication; 4.5 Dedekind's fundamental theorem Complex Numbers:; 5.1 Definition; 5.2 Addition; 5.3 Multiplication; 5.4 Subtraction; 5.5 Division; 5.6 Complex conjugates; 5.7 Absolute value; 5.8 Sums and products; 5.9 Powers; 5.10 Incorporation of the real numbers into the system of complex numbers.