Why doesn’t the diagonal argument used in example 11 .1 .4 show that the rationals are also uncountable? Concept Introduction: If a set x is one to one correspondence with natural numbers, then x is said to be countable. Otherwise x is uncountable. The rational number is considered to be countable but the real numbers are not and the diagonal argument is used to show that the real number is uncountable.

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Answer 1

Question

Chapter 11.1, Problem 1E

Interpretation Introduction

Interpretation:

Why doesn’t the diagonal argument used in example 11.1.4 show that the rationals are also uncountable?

Concept Introduction:

If a set x is one to one correspondence with natural numbers, then x is said to be countable. Otherwise x is uncountable.

The rational number is considered to be countable but the real numbers are not and the diagonal argument is used to show that the real number is uncountable.

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Answer 2

Question

Chapter 11.1, Problem 1E

Interpretation Introduction

Interpretation:

Why doesn’t the diagonal argument used in example 11.1.4 show that the rationals are also uncountable?

Concept Introduction:

If a set x is one to one correspondence with natural numbers, then x is said to be countable. Otherwise x is uncountable.

The rational number is considered to be countable but the real numbers are not and the diagonal argument is used to show that the real number is uncountable.

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Answer 3

Question

Chapter 11.1, Problem 1E

Interpretation Introduction

Interpretation:

Why doesn’t the diagonal argument used in example 11.1.4 show that the rationals are also uncountable?

Concept Introduction:

If a set x is one to one correspondence with natural numbers, then x is said to be countable. Otherwise x is uncountable.

The rational number is considered to be countable but the real numbers are not and the diagonal argument is used to show that the real number is uncountable.

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Answer 4

Question

Chapter 11.1, Problem 1E

Interpretation Introduction

Interpretation:

Why doesn’t the diagonal argument used in example 11.1.4 show that the rationals are also uncountable?

Concept Introduction:

If a set x is one to one correspondence with natural numbers, then x is said to be countable. Otherwise x is uncountable.

The rational number is considered to be countable but the real numbers are not and the diagonal argument is used to show that the real number is uncountable.

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Answer 5

Chapter 11.1, Problem 1E

Interpretation Introduction

Interpretation:

Why doesn’t the diagonal argument used in example 11.1.4 show that the rationals are also uncountable?

Concept Introduction:

If a set x is one to one correspondence with natural numbers, then x is said to be countable. Otherwise x is uncountable.

The rational number is considered to be countable but the real numbers are not and the diagonal argument is used to show that the real number is uncountable.

Answer 6

Chapter 11.1, Problem 1E

Interpretation Introduction

Interpretation:

Why doesn’t the diagonal argument used in example 11.1.4 show that the rationals are also uncountable?

Concept Introduction:

If a set x is one to one correspondence with natural numbers, then x is said to be countable. Otherwise x is uncountable.

The rational number is considered to be countable but the real numbers are not and the diagonal argument is used to show that the real number is uncountable.

Answer 7

Chapter 11.1, Problem 1E

Interpretation Introduction

Interpretation:

Why doesn’t the diagonal argument used in example 11.1.4 show that the rationals are also uncountable?

Concept Introduction:

If a set x is one to one correspondence with natural numbers, then x is said to be countable. Otherwise x is uncountable.

The rational number is considered to be countable but the real numbers are not and the diagonal argument is used to show that the real number is uncountable.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.2 - Prob. 1E Ch. 11.2 - Prob. 2E Ch. 11.2 - Prob. 3E

Solution Summary: The author explains that the diagonal argument does not prove that a set of objects is countably infinite if the elements can be placed in 1-1 correspondence with integers.

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