Real Numbers Chapter Overview

To define real numbers out of the blue

To construct real numbers from rational numbers (correct)

To introduce rational Cauchy sequences

To show that real numbers can be defined as limits of certain sequences

Rational Cauchy sequences (correct)

Rational sequences

Limits of certain sequences

Equivalence classes of sequences

That rational Cauchy sequences form a ring

That rational Cauchy sequences form an ideal (correct)

That rational Cauchy sequences tend to 0

That real numbers can be defined as limits