e are some notes on introductory real analysis. They cover the properties of the real numbers, sequences and series of real numbers, limits of functions, …

Feb 5, 2010 · Section 1.3 is devoted to elementary set the-ory and the topology of the real line, ending with the Heine-Borel and Bolzano-Weierstrass …

A real number x is said to be positive if it has a representative Cauchy sequence (xn)n2N 2 Q+ consisting entirely of positive rational numbers. We denote …

Under the identification of Q with a subset of R, the cut defining a real number consists of all rational numbers less than the given real number. The set …

The foundations of real analysis are given by set theory, and the notion of cardinality in set theory, as well as the axiom of choice, occur frequently in …

In this Chapter 0 we will review in detail the notation and background information that will be assumed throughout Chapters 1–9 of the main text (though …

of A and in B. It. two . table This. notion of. et, th. s of a . is dened as. distance functio. or metric .