eBook - ePub
An Introduction to Real Analysis
Ravi P. Agarwal, Cristina Flaut, Donal O'Regan
This is a test
Share book
- 277 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
An Introduction to Real Analysis
Ravi P. Agarwal, Cristina Flaut, Donal O'Regan
Book details
Book preview
Table of contents
Citations
About This Book
This book provides a compact, but thorough, introduction to the subject of Real Analysis. It is intended for a senior undergraduate and for a beginning graduate one-semester course.
Frequently asked questions
How do I cancel my subscription?
Can/how do I download books?
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
What is the difference between the pricing plans?
Both plans give you full access to the library and all of Perlegoâs features. The only differences are the price and subscription period: With the annual plan youâll save around 30% compared to 12 months on the monthly plan.
What is Perlego?
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, weâve got you covered! Learn more here.
Do you support text-to-speech?
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Is An Introduction to Real Analysis an online PDF/ePUB?
Yes, you can access An Introduction to Real Analysis by Ravi P. Agarwal, Cristina Flaut, Donal O'Regan in PDF and/or ePUB format, as well as other popular books in Mathematik & Mathematik Allgemein. We have over one million books available in our catalogue for you to explore.
Information
Chapter 1
Logic and Proof Techniques
We begin this chapter with the definition of mathematical statements, and introduce some logical connectives that we will use frequently in this book. We will also discuss some commonly used methods to prove mathematical results.
By a mathematical statement or proposition, we mean an unambiguous composition of words that is true or false. For example, two plus two is four is a true statement, and two plus three is seven is a false statement. However, x â y = y â x is not a proposition, because the symbols are not defined. If x â y = y â x for all x, y real numbers, then this is a false proposition; if x â y = y â x for some real numbers, then this is a true proposition. Help me please, and your place or mineâare also not statements. A single letter is always used to denote a statement. For example, the letter p may be used for the statement eleven is an even number. Thus, p:11 is an even number. A statement is said to have truth value T or F according as the statement is true or false. For example, the truth value of p:1 + 2 + ⊠+ 10 = 55 is T, whereas for p:12 + 22 + 32 = 15 is F. The knowledge of truth value of a statement enables us to replace it by some other âequivalentâ statement. From given statements, new statements can be produced by using the following standard logical connectives:
1. Negation, ~:If p is a statement, then its negation ~ p is the statement not p. Thetruth valueof ~ p is F or T according as the truth value of p is T or F. Thus, if p: seven is even number, then ~ p: seven is not an even number, or seven is an odd number.
2. Implication, â: If from a statement p another statement q follows, we say p implies q and write p â q. The truth value of p â q is F only when p has truth value T and q has the truth value F. For example, x = 7 â x2 = 49. If n is an even integer, then n + 1 is an odd integer.
3. Conjuction, â§: The statement p and q is denoted as p ⧠q and is called the conjunction of the statements p a...