4.4: Number Lines and Interval Notation

Front

What is interval notation?

Back

Interval notation is a mathematical notation used to represent a range of values on a number line. It uses parentheses and brackets to indicate whether endpoints are included or excluded.

Front

What does the notation \( (a, b) \) represent?

Back

The notation \( (a, b) \) represents an open interval, meaning that the endpoints \( a \) and \( b \) are not included in the interval.

Front

What does the notation \( [a, b] \) represent?

Back

The notation \( [a, b] \) represents a closed interval, meaning that the endpoints \( a \) and \( b \) are included in the interval.

Front

What does the notation \( (a, b] \) represent?

Back

The notation \( (a, b] \) represents a half-open interval, meaning that the endpoint \( a \) is not included, while \( b \) is included.

Front

What does the notation \( [a, b) \) represent?

Back

The notation \( [a, b) \) represents a half-open interval, meaning that the endpoint \( a \) is included, while \( b \) is not included.

Front

How is \( (-\, ext{infinity}, b) \) interpreted in interval notation?

Back

The notation \( (-\, ext{infinity}, b) \) represents all real numbers less than \( b \), with \( b \) not included.

Front

How is \( [a, + ext{infinity}) \) interpreted in interval notation?

Back

The notation \( [a, + ext{infinity}) \) represents all real numbers greater than or equal to \( a \).

Front

What is the difference between open and closed intervals?

Back

Open intervals do not include their endpoints, while closed intervals do include their endpoints.

Front

Convert the solution \( x < 1 \) into interval notation.

Back

The solution in interval notation is \( (-\, ext{infinity}, 1) \).

Front

Convert the solution \( x \geq -2 \) into interval notation.

Back

The solution in interval notation is \( [-2, + ext{infinity}) \).