#
Interval and List Notation

The concepts for this lesson are summarized in
Introduction to Sets.

Recall:

Braces look like
$\,\{\;\;\}\,$
and are used for
list notation.

Parentheses look like
$\,(\;\;)\,$
and are used in
interval notation
when an endpoint IS NOT included.

Brackets look like
$\,[\;\;\;]\,$
and are used in interval notation when an endpoint IS included.

## Examples

Question:
Is
$\,2\,$ in the set
$\,(2,3)\,$?

Solution:
No.
The parenthesis next to the
$\,2\,$ indicates that
$\,2\,$ is *not* included.

Question:
Is
$\,2\,$ in the set
$\,[2,3)\,$?

Solution:
Yes.
The bracket next to the
$\,2\,$ indicates that
$\,2\,$ *is* included.

Question:
Is
$\,2.5\,$ in the set
$\,(2,3)\,$?

Solution:
Yes.
The interval
$\,(2,3)\,$ contains all real numbers
between $\,2\,$ and $\,3\,,$
but does not include either endpoint.

Question:
Is
$\,2\,$ in the set
$\,\{2,3\}\,$?

Solution:
Yes.
This set has two members:
the number
$\,2\,,$ and the number $\,3\,.$
The braces indicate that list notation is being used here.

Question:
Is
$\,100\,$ in the set
$\,\{1,2,3,\ldots\}\,$?

Solution:
Yes.
The ‘$\,\ldots\,$’ indicates
that the established pattern continues ad infinitum.
This set contains all positive integers.

Question:
Is
$\,100.5\,$ in the set
$\,\{1,2,3,\ldots\}\,$?

Solution:
No.
The number
$\,100.5\,$ is not an integer.

Question:
Is
$\,100.5\,$ in the set
$\,(2,\infty)\,$?

Solution:
Yes.
This set contains all real numbers strictly greater than $\,2\,.$

Question:
Is
$\,2\,$ in the set
$\,(-\infty,2)\,$?

Solution:
No.
The parenthesis next to the
$\,2\,$ indicates that $\,2\,$ is *not* included.

Question:
Is
$\,2\,$ in the set
$\,(-\infty,2]\,$?

Solution:
Yes.
The bracket next to the
$\,2\,$ indicates that $\,2\,$ *is* included.

Question:
Is
$\,1.9999\,$ in the set
$\,(-\infty,2)\,$?

Solution:
Yes.
This interval contains all real numbers less than $\,2\,.$

## Practice

Type **yes** or **no** (all lowercase) for your answers.