whats interval notation?
Interval notation is a method of writing down a set of numbers. Usually, this is used to describe a certain span or group of spans of numbers along a axis, such as an x-axis. However, this notation can be used to describe any group of numbers.
For example, consider the set of numbers that are all greater than 5. If we were to write an inequality for this set, letting x be any number in the group, we would say:
x>5
Interval notation is a way to express intervals, which are a range of numbers along a number line. It is a compact and convenient way to represent a set of numbers without explicitly listing all the values.
In interval notation, an interval is written using parentheses or brackets and separated by a comma.
There are four types of interval notation:
1. Open Interval: An open interval does not include the endpoints. It is represented by using parentheses. For example, (a, b) represents all numbers between a and b, excluding a and b.
2. Closed Interval: A closed interval includes both endpoints. It is represented by using brackets. For example, [a, b] represents all numbers between a and b, including a and b.
3. Half-Open Interval: A half-open interval includes one endpoint but not the other. It is represented by combining the concepts of open and closed intervals. For example, (a, b] represents all numbers between a and b, excluding a but including b.
4. Half-Closed Interval: A half-closed interval includes one endpoint but not the other, with the opposite configuration of a half-open interval. For example, [a, b) represents all numbers between a and b, including a but excluding b.
To use interval notation, you need to identify the endpoints of the interval and determine whether they are included or excluded. Then, you can write the interval using the appropriate parentheses or brackets.
For example, if you have an interval from 2 to 6, including both endpoints, the interval notation would be [2, 6]. If the interval is from -3 to 5, including -3 but excluding 5, the interval notation would be [-3, 5).