# Set Theory: A First Course by Daniel W. Cunningham

Author:Daniel W. Cunningham

Language: eng

Format: epub

Publisher: Cambridge University Press

Published: 2016-06-21T04:00:00+00:00

Corollary 5.2.7. A set is countably infinite if and only if there is a bijection .

Proof. If is countably infinite, then Theorem 5.2.6 implies that there exists a bijection . Conversely, suppose that is a bijection. Since is one-to-one, is infinite by Corollary 5.1.11. As is onto , Theorem 3.3.18 asserts the existence of the inverse function that is one-to-one. Hence, is countable and infinite. ☐

Theorem 5.2.8. If is a countably infinite set, then there exists an enumeration of all the elements in such that each element in appears in this enumeration exactly once.

**Download**

**Copyright Disclaimer:**

This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.

**Categories**

**Popular ebooks**

The Black Swan by Nassim Nicholas Taleb(747)

Practical Guide To Principal Component Methods in R (Multivariate Analysis Book 2) by Alboukadel Kassambara(376)

Harry Potter 02 & The Chamber Of Secrets (Illustrated) by J.K. Rowling(275)

Weapons of Math Destruction by Cathy O'Neil(228)

Easy Algebra Step-by-Step by Sandra Luna McCune(178)

Once Upon an Algorithm by Martin Erwig(167)

The Book of Numbers by Peter Bentley(157)

Applied Predictive Modeling by Max Kuhn & Kjell Johnson(155)

The Black Swan the Impact of the Highly Improbable by Nassim Nicholas Taleb(146)

Plain Plane Geometry by Amol Sasane(141)

A Mind For Numbers: How to Excel at Math and Science (Even If You Flunked Algebra) by Barbara Oakley(128)

The Great Unknown by Marcus du Sautoy(125)

Introducing Relativity by Bruce Bassett(121)

Math and Science Workout for the ACT by Princeton Review(106)

The Manga Guide to Calculus by Hiroyuki Kojima & Shin Togami & Becom Co. Ltd(105)

Statistical Modeling: A Fresh Approach (Project MOSAIC Books) by Daniel Kaplan(101)

TCP IP by Todd Lammle(101)

Finite Element Concepts by Gautam Dasgupta(99)

Descartes' Error by Antonio Damasio(98)