Introduction to Set theory: Difference between revisions
Thakshashila (talk | contribs) Created page with "= Introduction to Set Theory = Set theory is a fundamental topic in mathematics that deals with the study of '''sets''', which are collections of '''distinct''' and '''well-defined objects'''. It is the foundation for many advanced topics in mathematics and logic. == What is a Set? == A '''set''' is a collection of objects, called '''elements''' or '''members''', that are grouped together because they share a common property. * Example: A set of vowels in the English..." |
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== Types of Sets == | == Types of Sets == | ||
* | * [[Finite Set]] – Contains a countable number of elements. | ||
* Example: <math>\{2, 4, 6, 8\}</math> | * Example: <math>\{2, 4, 6, 8\}</math> | ||
* | * [[Infinite Set]] – Has uncountably many elements. | ||
* Example: <math>\{1, 2, 3, 4, \ldots\}</math> | * Example: <math>\{1, 2, 3, 4, \ldots\}</math> | ||
* | * [[Empty Set]] ('''Null Set''') – A set with no elements. | ||
* Notation: <math>\emptyset</math> or <math>\{\}</math> | * Notation: <math>\emptyset</math> or <math>\{\}</math> | ||
* | * [[Singleton Set]] – A set with only one element. | ||
* Example: <math>\{7\}</math> | * Example: <math>\{7\}</math> | ||
* | * [[Equal Sets]] – Two sets with exactly the same elements. | ||
* Example: <math>A = \{1, 2, 3\}, B = \{3, 2, 1\} \Rightarrow A = B</math> | * Example: <math>A = \{1, 2, 3\}, B = \{3, 2, 1\} \Rightarrow A = B</math> | ||