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.

Example 3.2.1

\([2,5)\)

Solution

Figure 3.2.1

In the example above, the interval starts with a left bracket and ends with a parentheses. Hence,the interval includes the number 2 and does not include the number 5. By observing the corresponding number a closed bullet \(\bullet\) is used to demonstrate that the number 2 is included in the interval, on the other hand an open bullet \(\circ\) is on the number 5 to demonstrate that 5 in not in the interval. Some of the numbers in the set include 2, 2.5, 3.4, 4 and 4.99. Again, the number 5 is not in this set.

Example 3.2.2

\([-4,10)\)

Solution

Figure 3.2.2

Similar to example 1, the endpoint on the left which corresponds to the number -4 is included in the interval, while the endpoint on the right is not included in the interval. Some numbers on the interval above are -4, -2, 0, 3.5, 8.5 and 9.9.

Exercise 3.2.1

Draw a number line for the following intervals and list at least three numbers inside the set.

1. \([-3,1)\)
2. \([-12,-2)\)
3. \([-233,-223)\)
4. \([3.5,5)\)
5. \([0,1)\)
6. \([-1.4,2.8)\)