Anonymous
Dec 7, 2023
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Dec 7, 2023
An open interval is a set of real numbers between two specified endpoints, excluding the endpoints themselves. It is denoted by using parentheses. For example, (2, 5) represents all real numbers greater than 2 and less than 5, but does not include 2 and 5.
A closed interval, on the other hand, includes the endpoints. It is denoted by using square brackets. For example, [2, 5] represents all real numbers greater than or equal to 2 and less than or equal to 5.
To summarize:
- Open interval: (a, b) includes all real numbers greater than a and less than b, excluding a and b.
- Closed interval: [a, b] includes all real numbers greater than or equal to a and less than or equal to b, including a and b.
Example:
Consider the interval (1, 4). This represents all real numbers greater than 1 and less than 4, but does not include 1 and 4. So, the interval can be written as: 1 < x < 4.
Now, consider the interval [1, 4]. This represents all real numbers greater than or equal to 1 and less than or equal to 4, including 1 and 4. So, the interval can be written as: 1 ≤ x ≤ 4.
A closed interval, on the other hand, includes the endpoints. It is denoted by using square brackets. For example, [2, 5] represents all real numbers greater than or equal to 2 and less than or equal to 5.
To summarize:
- Open interval: (a, b) includes all real numbers greater than a and less than b, excluding a and b.
- Closed interval: [a, b] includes all real numbers greater than or equal to a and less than or equal to b, including a and b.
Example:
Consider the interval (1, 4). This represents all real numbers greater than 1 and less than 4, but does not include 1 and 4. So, the interval can be written as: 1 < x < 4.
Now, consider the interval [1, 4]. This represents all real numbers greater than or equal to 1 and less than or equal to 4, including 1 and 4. So, the interval can be written as: 1 ≤ x ≤ 4.
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