3: Interval Notation
- Page ID
- 45156
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Interval notation is used to describe a group of numbers in the number line. In mathematics these groups are called Sets. The interval notation is used to group all the numbers between two numbers being studied. The notation used to describe a set are the following.
| Symbols used | |
| ( | used to start interval |
| [ | used to start interval |
| ) | used to end interval |
| ] | used to end interval |
These symbols can be used in different combinations. The combinations have meaning and this section will teach how to successfully use these symbols to describe any desired set. Note: number on the left side should always be less than the number on the right side (Incorrect : (5,2) ).
- 3.1: [a, b]
- This section will focus on intervals in the form [ , ]. By observation, the interval begins and ends with brackets. The use of brackets implies that the endpoints are being included in the set. This section will include the endpoint on the right and the endpoint on the left since again the interval notation starts and ends with brackets.
- 3.2: [a, b)
- This section will study intervals in the form [a,b). The interval begins with a left bracket and ends with a right parentheses. Starting the interval with a brackets means the right endpoint is included in the set and ending with the use of a parentheses means the left endpoint in not included.
- 3.3: (a, b]
- The notation in this section looks similar to the previous section, but they are not same. By looking at the notation closer it becomes clear that the endpoint on the left is not included in the set while the endpoint on the right is included in the interval.
- 3.4: (a, b)
- In this section, both endpoints are not included in the interval.
- 3.5: Interval Notation and Infinity
- What is infinity? Infinity is not a real number. Infinity is larger than any number that can be imagined. It is an idea of having no bounds. A line is an example of having no bounds. For instance the number line has arrows at the end to represent this idea of having no bounds.