Interval notations

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Intros
Lessons
  1. How many ways are there to represent interval?
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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
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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".