1. Home
  2. >Algebra
  3. >Set Theory
Help

Interval notations

Everything You Need in One Place

Homework problems? Exam preparation? Trying to grasp a concept or just brushing up the basics? Our extensive help & practice library have got you covered.

Learn and Practice With Ease

Our proven video lessons ease you through problems quickly, and you get tonnes of friendly practice on questions that trip students up on tests and finals.

Instant and Unlimited Help

Our personalized learning platform enables you to instantly find the exact walkthrough to your specific type of question. Activate unlimited help now!

Get the most by viewing this topic in your current grade. Pick your course now.

?
Intros
Lessons
  1. How many ways are there to represent interval?
?
Examples
Lessons
  1. Expressing Intervals Using a Number Line
    Express the following intervals on the given number line:
    number line
    1. x is greater than - 4.
    2. a is less than or equal to 6.
    3. k is less than 2 OR greater than or equal to 8.
Topic Notes
?

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".