Introducción a la Teoría de Conjuntos

What is Set Theory?

• Set theory is a way to group and organize objects or things.
• It's like putting toys away in a toy box, but instead of toys, we're working with numbers, shapes, or other things.

Basic Concepts

• Set: A collection of unique objects, called elements or members.
• Element: A single object in a set.
• Member: Another word for element.

Set Notation

• We use curly brackets { } to show a set.
• For example, {1, 2, 3, 4, 5} is a set of numbers from 1 to 5.

Types of Sets

• Empty Set: A set with no elements, denoted by { } or ∅.
• Singleton Set: A set with only one element, e.g. {5}.
• Finite Set: A set with a limited number of elements, e.g. {1, 2, 3, 4, 5}.
• Infinite Set: A set with an endless number of elements, e.g. all natural numbers.

Set Operations

• Union: Combining two or more sets to get all the elements, denoted by ∪.
• Intersection: Finding the elements common to two or more sets, denoted by ∩.
• Difference: Finding the elements in one set that are not in another set, denoted by -.

Examples

• Union: {1, 2, 3} ∪ {3, 4, 5} = {1, 2, 3, 4, 5}
• Intersection: {1, 2, 3} ∩ {3, 4, 5} = {3}
• Difference: {1, 2, 3} - {3, 4, 5} = {1, 2}

Fun Activities

• Create a set of your favorite toys or books.
• Draw a Venn diagram to show the union and intersection of two sets.
• Play a game where you identify elements in a set or find the difference between two sets.