Discrete Mathematics - Vol 2 | 3. Countable and Uncountable Sets by Abraham | Learn Smarter
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3. Countable and Uncountable Sets

The discussion focuses on the concepts of cardinality in sets, distinguishing between finite and infinite sets. The chapter categorizes infinite sets into countable and uncountable, explaining the definition of countable sets and providing examples and bijections for various sets. It concludes with the significance of understanding these classifications in mathematics.

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Sections

  • 3

    Countable And Uncountable Sets

    This section provides an introduction to the concepts of countable and uncountable sets, particularly focusing on cardinality and distinctions in types of infinite sets.

    Learning Practice

  • 3.1

    Cardinality Of Finite Sets

    This section discusses the concept of cardinality, specifically for finite sets, and introduces definitions along with examples that illustrate the cardinality of such sets.

    Learning Practice

  • 3.2

    Cardinality Of Infinite Sets

    This section explores the concept of cardinality in both finite and infinite sets, highlighting the differences between countable and uncountable sets.

    Learning Practice

  • 3.3

    Definition Of Countable Sets

    Countable sets are defined as those that are either finite or have the same cardinality as the set of positive integers.

    Learning Practice

  • 3.4

    Countably Finite Sets And Countably Infinite Sets

    This section covers the concepts of countably finite and countably infinite sets, including their definitions, significance, and examples.

    Learning Practice

  • 3.5

    Theorem On Countable Sets

    This section discusses the concept of countable sets, including finite and countably infinite sets, and introduces a theorem regarding countability.

    Learning Practice

  • 3.6

    Examples Of Countably Finite Sets

    This section discusses countably finite sets, exploring their properties and providing examples that illustrate cardinality comparisons.

    Learning Practice

  • 3.7

    Set Of Odd Positive Integers

    This section explores the concept of countable sets, focusing primarily on the set of odd positive integers and its cardinality compared to the set of positive integers.

    Learning Practice

  • 3.8

    Set Of Integers

    This section discusses the cardinality of finite and infinite sets, focusing on countable and uncountable sets.

    Learning Practice

  • 3.9

    Set Of Prime Numbers

    This section discusses the set of prime numbers, defining what they are and demonstrating their countability.

    Learning Practice

References

ch27.pdf

Class Notes

Memorization

What we have learnt

  • The cardinality of a set is...
  • Countable sets can be finit...
  • A set is countably infinite...

Final Test

Revision Tests