If it is possible to label each element of an infinite set S with a finite string of keyboard characters, from a finite list characters, where no two elements of S have the same label, then S is a countably infinite set. Use the above statement and prove that the set of rational numbers is countable. Multiple Choice We can label the rational numbers with strings from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, /,-) by writing down the string that represents that rational number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable. We can label the rational numbers with strings from the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, /) by writing down the string that represents that rational number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable. We can label the rational numbers with strings from the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -] by writing down the string that represents that rational number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable. We can label the rational numbers with strings from the set (1, 2, 3, 4, 5, 6, 7, 8, 9, /,-) by writing down the string that represents that rational number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable.
If it is possible to label each element of an infinite set S with a finite string of keyboard characters, from a finite list characters, where no two elements of S have the same label, then S is a countably infinite set. Use the above statement and prove that the set of rational numbers is countable. Multiple Choice We can label the rational numbers with strings from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, /,-) by writing down the string that represents that rational number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable. We can label the rational numbers with strings from the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, /) by writing down the string that represents that rational number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable. We can label the rational numbers with strings from the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -] by writing down the string that represents that rational number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable. We can label the rational numbers with strings from the set (1, 2, 3, 4, 5, 6, 7, 8, 9, /,-) by writing down the string that represents that rational number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable.
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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![If it is possible to label each element of an infinite set S with a finite string of keyboard characters, from a finite list characters, where no two elements of S
have the same label, then S is a countably infinite set.
Use the above statement and prove that the set of rational numbers is countable.
Multiple Choice
We can label the rational numbers with strings from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, /,-) by writing down the string that represents that rational
number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable.
We can label the rational numbers with strings from the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, /) by writing down the string that represents that rational
number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable.
We can label the rational numbers with strings from the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -] by writing down the string that represents that rational
number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable.
We can label the rational numbers with strings from the set (1, 2, 3, 4, 5, 6, 7, 8, 9, /,-) by writing down the string that represents that rational
number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbcc04df1-376c-4e8a-b5a8-f3205317476f%2Fe42a100b-99f1-4c8c-b535-8a6d24ed906a%2F6qzagsu_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If it is possible to label each element of an infinite set S with a finite string of keyboard characters, from a finite list characters, where no two elements of S
have the same label, then S is a countably infinite set.
Use the above statement and prove that the set of rational numbers is countable.
Multiple Choice
We can label the rational numbers with strings from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, /,-) by writing down the string that represents that rational
number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable.
We can label the rational numbers with strings from the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, /) by writing down the string that represents that rational
number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable.
We can label the rational numbers with strings from the set (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, -] by writing down the string that represents that rational
number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable.
We can label the rational numbers with strings from the set (1, 2, 3, 4, 5, 6, 7, 8, 9, /,-) by writing down the string that represents that rational
number in its simplest form. As the labels are unique, it follows that the set of rational numbers is countable.
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