Interval and List Notation

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 $\,2\,$.

(an even number, please)