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Algebra: Structure And Method, Book 1

(REV)00th Edition

ISBN:9780395977224

Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Chapter2: Working With Real Numbers

Section2.1: Basic Assumptions

Problem 40WE

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Question

Determine whether each of these sets is finite, countably infinite, or uncountable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set.

The real numbers between 0 and 2 (Multiple choice)

A. The set is countably infinite with one-to-one correspondence 1 ↔ 0, 2 ↔ 0.00001,3 ↔ 0.00002, and so on.

B. The set is finite.

C. The set is countably infinite with one-to-one correspondence 1 ↔ 0.00001, 2 ↔ 0.00002, 3 ↔ 0.00003, and so on.

D.The set is uncountable.

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