Interval notations  Set Theory
Interval notations
Lessons
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
 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:
 Number line
 Inequalities (arrows)
 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:
 > to denote greater than, above
 < to denote less than, below
 ≥ to denote greater than or equal to, at least, no less than, minimum
 ≤ 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".

Intro Lesson

1.
Expressing Intervals Using a Number Line
Express the following intervals on the given number line: