INTERVAL and LIST NOTATION

Recall:
Braces look like [beautiful math coming... please be patient] $\,\{\;\;\}\,$ and are used for list notation.
Parentheses look like [beautiful math coming... please be patient] $\,(\;\;)\,$ and are used in interval notation when an endpoint IS NOT included.
Brackets look like [beautiful math coming... please be patient] $\,[\;\;\;]\,$ and are used in interval notation when an endpoint IS included.

EXAMPLES:
Question: Is [beautiful math coming... please be patient] $\,2\,$ in the set [beautiful math coming... please be patient] $\,(2,3)\,$?
Solution: No.
The parenthesis next to the [beautiful math coming... please be patient] $\,2\,$ indicates that [beautiful math coming... please be patient] $\,2\,$ is not included.
Question: Is [beautiful math coming... please be patient] $\,2\,$ in the set [beautiful math coming... please be patient] $\,[2,3)\,$?
Solution: Yes.
The bracket next to the [beautiful math coming... please be patient] $\,2\,$ indicates that [beautiful math coming... please be patient] $\,2\,$ is included.
Question: Is [beautiful math coming... please be patient] $\,2.5\,$ in the set [beautiful math coming... please be patient] $\,(2,3)\,$?
Solution: Yes.
The interval [beautiful math coming... please be patient] $\,(2,3)\,$ contains all real numbers between $\,2\,$ and $\,3\,$, but does not include either endpoint.
Question: Is [beautiful math coming... please be patient] $\,2\,$ in the set [beautiful math coming... please be patient] $\,\{2,3\}\,$?
Solution: Yes.
This set has two members: the number [beautiful math coming... please be patient] $\,2\,$, and the number $\,3\,$.
The braces indicate that list notation is being used here.
Question: Is [beautiful math coming... please be patient] $\,100\,$ in the set [beautiful math coming... please be patient] $\,\{1,2,3,\ldots\}\,$?
Solution: Yes.
The “$\,\ldots\,$” indicates that the established pattern continues ad infinitum.
This set contains all positive integers.
Question: Is [beautiful math coming... please be patient] $\,100.5\,$ in the set [beautiful math coming... please be patient] $\,\{1,2,3,\ldots\}\,$?
Solution: No.
The number [beautiful math coming... please be patient] $\,100.5\,$ is not an integer.
Question: Is [beautiful math coming... please be patient] $\,100.5\,$ in the set [beautiful math coming... please be patient] $\,(2,\infty)\,$?
Solution: Yes.
This set contains all real numbers strictly greater than $\,2\,$.
Question: Is [beautiful math coming... please be patient] $\,2\,$ in the set [beautiful math coming... please be patient] $\,(-\infty,2)\,$?
Solution: No.
The parenthesis next to the [beautiful math coming... please be patient] $\,2\,$ indicates that $\,2\,$ is not included.
Question: Is [beautiful math coming... please be patient] $\,2\,$ in the set [beautiful math coming... please be patient] $\,(-\infty,2]\,$?
Solution: Yes.
The bracket next to the [beautiful math coming... please be patient] $\,2\,$ indicates that $\,2\,$ is included.
Question: Is [beautiful math coming... please be patient] $\,1.9999\,$ in the set [beautiful math coming... please be patient] $\,(-\infty,2)\,$?
Solution: Yes.
This interval contains all real numbers less than $\,2\,$.
Master the ideas from this section
by practicing the exercise at the bottom of this page.

When you're done practicing, move on to:
Introduction to Variables

 
 

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