Abstract
While we were talking about sequences, we noted that care needs to be taken in distinguishing the sequence (a n ) from the set of its terms {a n }. We will say that the sequence (a n ) lists the elements of H if H = { a n }. (The elements of the set H and thus the terms of (a n ) can be arbitrary; we do not restrict ourselves to sequences of real numbers.)
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
Davidson, K.R., Dosig, A.P.: Real Analysis and Applications. Theory in Practice. Springer, New York (2010)
Erdős, P., Surányi, J.: Topics in the Theory of Numbers. Springer, New York (2003)
Euclid: The Thirteen Books of the Elements [Translated with introduction and commentary by Sir Thomas Heath]. Second Edition Unabridged. Dover, New York (1956)
Hewitt, E., Stromberg, K.: Real and Abstract Analysis. Springer, New York (1975)
Niven, I., Zuckerman, H.S., Montgomery, H.L.: An Introduction to the Theory of Numbers, 5th edn. Wiley, New York (1991)
Rademacher, H., Toeplitz, O.: Von Zahlen und Figuren. Springer, Berlin (1933) [English translation: The Enjoyment of Mathematics]. Dover, New York (1990)
Rudin, W.: Principles of Mathematical Analysis, 3rd edn. McGraw-Hill, New York (1976)
Zaidman, S.: Advanced Calculus. An Introduction to Mathematical Analysis. World Scientific, Singapore (1997)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer New York
About this chapter
Cite this chapter
Laczkovich, M., Sós, V.T. (2015). Countable Sets. In: Real Analysis. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2766-1_8
Download citation
DOI: https://doi.org/10.1007/978-1-4939-2766-1_8
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4939-2765-4
Online ISBN: 978-1-4939-2766-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)