# Interval notations

### Interval notations

#### Lessons

In this lesson, we will learn:

• Expressing Intervals Using a Number Line
• Expressing Intervals Using Inequalities
• Expressing Intervals Using Interval Notations
• Simplifying Multiple Notations
• Interchanging Between Number Lines, Inequalities and Interval Notations
Notes:

• Interval: all the numbers in between two numbers.
• Interval notation: a notation for representing an interval as a pair of numbers which are the endpoints of the interval.
• Intervals can be represented in 3 ways:
1. Number line
2. Inequalities (arrows)
3. Interval notations (brackets)
• For a number line, we use a closed circle "•" to represent end points being included and an open circle "°" to represent end points not being included.
• For inequalities, we use the following symbols:
1. > to denote greater than, above
2. < to denote less than, below
3. ≥ to denote greater than or equal to, at least, no less than, minimum
4. ≤ to denote less than or equal to, at most, no more than, maximum
• For interval notations, we use a square bracket " [ ] " to represent end points being included and a round bracket or a parenthesis " ( ) " to represent end points not being included.
• Infinity is not a number, so we can NEVER include it. Hence, we can only use round brackets for infinity.
• If we want to represent 2 intervals using interval notations, we have to use "∩" to denote "and/intersection" and "∪" to denote "or/union".
• Introduction
a)
How many ways are there to represent interval?

• 1.
Expressing Intervals Using a Number Line
Express the following intervals on the given number line:
a)
x is greater than - 4.

b)
a is less than or equal to 6.

c)
k is less than 2 OR greater than or equal to 8.