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 that are multiples of 10 (Check all that apply.) [] The set is countably finite with one-to-one correspondence 1 ↔ 0, 2 ↔ 10, 3 ↔ −10, 4 ↔ 20, 5 ↔ −20, 6 ↔ 30, and so on. [] The set is countably infinite with one-to-one correspondence 1 ↔ 0, 2 ↔ 10, 3 ↔ −10, 4 ↔ 20, 5 ↔ −20, 6 ↔ 30, and so on. [] The set is countably infinite with one-to-one correspondence n ↔ 10n. [] The set is uncountable.
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 that are multiples of 10 (Check all that apply.) [] The set is countably finite with one-to-one correspondence 1 ↔ 0, 2 ↔ 10, 3 ↔ −10, 4 ↔ 20, 5 ↔ −20, 6 ↔ 30, and so on. [] The set is countably infinite with one-to-one correspondence 1 ↔ 0, 2 ↔ 10, 3 ↔ −10, 4 ↔ 20, 5 ↔ −20, 6 ↔ 30, and so on. [] The set is countably infinite with one-to-one correspondence n ↔ 10n. [] The set is uncountable.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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 that are multiples of 10 (Check all that apply.)
[] The set is countably finite with one-to-one correspondence 1 ↔ 0, 2 ↔ 10, 3 ↔ −10, 4 ↔ 20, 5 ↔ −20, 6 ↔ 30, and so on.
[] The set is countably infinite with one-to-one correspondence 1 ↔ 0, 2 ↔ 10, 3 ↔ −10, 4 ↔ 20, 5 ↔ −20, 6 ↔ 30, and so on.
[] The set is countably infinite with one-to-one correspondence n ↔ 10n.
[] The set is uncountable.
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