# Interval notations

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##### Examples

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###### 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:
- 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".

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