Sets and Set Notation

A set is a collection of stuff. The stuff can be things like cows, cars, teddy bears or atoms in a solid. We call the collection of stuff elements of the set. Typically in mathematics the elements of a set are numbers.

A set is denoted by the curly brackets $\{$ and $\}$. For example, the set $A$ is all of the students in my math class. We would then write

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to denote the students using set notation.

Usually sets can be too big to write. For example, write down the set of all people living in your country. However, we do have a method of denoting large sets. For example, we would say

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The basic idea is to write the set as <Sign in to see all the formulas> where $P$ is some characteristic that describes $x$.

Here are some more examples:

Set	Notation
Set of positive integers.	<Sign in to see all the formulas>
Set of all integers.	<Sign in to see all the formulas>
Set of all real numbers greater than 2.	<Sign in to see all the formulas>
Set of all rational numbers.	<Sign in to see all the formulas>
The set of all real numbers between $-2$ and $3$.	<Sign in to see all the formulas>
The set with no elements.	We call this the empty set and denote it by <Sign in to see all the formulas>. In other words, <Sign in to see all the formulas>.

Finally, when a variable is in a set we use the symbol $\in$. For example, if $y$ is in the set $A$ then we would write

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Similarly, if $y$ is not in the set $A$ then we would write

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