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Feb 5, 2010 · An inﬁnite sequence (more brieﬂy, a sequence) of

**real**numbers is a**real**-valued function deﬁned on a set of integers ˚ n ˇ ˇn k. We call the values of the functionthe terms of the sequence. We denote a sequence by listingitsterms inorder; thus, fsng. 1 kDfsk;skC1;:::g: (4.1.1) For example, ˆ 1 n2C1 ˙1 0.Abstract. These are some notes on introductory

**real****analysis**. They cover the properties of the**real**numbers, sequences and series of real numbers, limits of functions, continuity, differentiability, sequences and series of functions, and Riemann integration. They don’t include multi-variable calculus or contain any problem sets.ISBN: 9781718862401. [JL] = Basic

**Analysis**: Introduction to**Real****Analysis**(Vol. 1) (**PDF**- 2.2MB) by Jiří Lebl, June 2021 (used with permission) This book is available as a free**PDF**download. You can purchase a paper copy by following a link at the same site.**analysis**. Thus we begin with a rapid review of this theory. For more details see, e.g. [Hal]. We then discuss the**real**numbers from both the axiomatic and constructive point of view. Finally we discuss open sets and Borel sets. In some sense,**real analysis**is a pearl formed around the grain of sand provided by paradoxical sets.This version of Elementary

**Real****Analysis**, Second Edition, is a hypertexted**pdf**ﬁle, suitable for on-screen viewing. For a trade paperback copy of the text, with the same numbering of Theorems and Exercises (but with diﬀerent page numbering), please visit our web site. Direct all correspondence to thomson@sfu.ca.Abstract. These are some notes on introductory

**real****analysis**. They cover limits of functions, continuity, diﬀerentiability, and sequences and series of functions, but not Riemann integration A background in sequences and series of real numbers and some elementary point set topology of the real numbers0.2. ABOUT

**ANALYSIS**7 0.2 About**analysis****Analysis**is the branch of mathematics that deals with inequalities and limits. The present course deals with the most basic concepts in**analysis**. The goal of the course is to acquaint the reader with rigorous proofs in**analysis**and also to set a ﬁrm foundation for calculus of one variable (and several