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 integers with absolute value less than 1,000,000. (Check all that apply.) [] The set is countably infinite. [] The set is finite. [] The set is countably infinite with one-to-one correspondence 1 ↔ −1,999,999, 2 ↔ −1,999,998, 3 ↔ −1,999,997, and so on. [] The set is countably infinite with one-to-one correspondence 0 ↔ −1,999,999, 1 ↔ −1,999,998, 2 ↔ −1,999,997, and so on. [] The cardinality of the set is 1,999,999.
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 integers with absolute value less than 1,000,000. (Check all that apply.) [] The set is countably infinite. [] The set is finite. [] The set is countably infinite with one-to-one correspondence 1 ↔ −1,999,999, 2 ↔ −1,999,998, 3 ↔ −1,999,997, and so on. [] The set is countably infinite with one-to-one correspondence 0 ↔ −1,999,999, 1 ↔ −1,999,998, 2 ↔ −1,999,997, and so on. [] The cardinality of the set is 1,999,999.
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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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 integers with absolute value less than 1,000,000. (Check all that apply.)
[] The set is countably infinite.
[] The set is finite.
[] The set is countably infinite with one-to-one correspondence 1 ↔ −1,999,999, 2 ↔ −1,999,998, 3 ↔ −1,999,997, and so on.
[] The set is countably infinite with one-to-one correspondence 0 ↔ −1,999,999, 1 ↔ −1,999,998, 2 ↔ −1,999,997, and so on.
[] The cardinality of the set is 1,999,999.
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