Representation and Types of Sets

The basic vocabulary used to describe a collection of objects.

What is a Set?

A set is a well-defined collection of distinct objects, called its elements. If $x$ is an element of set $A$, we write $x \in A$.

Types of Sets

TypeDescription
Empty Set ($\emptyset$)Contains no elements
Finite SetHas a countable number of elements
Infinite SetHas an uncountable number of elements
Equal SetsContain exactly the same elements

Subsets and Intervals

If every element of $A$ is also in $B$, we say $A$ is a subset of $B$, written $A \subset B$. Intervals like $(a, b)$ and $[a, b]$ represent subsets of real numbers.

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