Consider the set \{x \mid x>2\} (in set-builder notation). Part 1 of 2. The set in interval notation is $\square$
Answer (2)
The set includes all numbers greater than 2.
Use a parenthesis to indicate that 2 is not included in the interval.
Use the infinity symbol to indicate that the interval extends indefinitely to the right.
The set in interval notation is ( 2 , ∞ ) .
Explanation
Understanding the Problem We are given a set defined in set-builder notation as all x such that x is greater than 2. Our goal is to express this set using interval notation.
Expressing the Set as an Interval In interval notation, we use parentheses '(' and ')' to indicate that the endpoint is not included in the interval, and brackets '[' and ']' to indicate that the endpoint is included. Since 2"> x > 2 , the value 2 is not included in the set. The set includes all numbers greater than 2, extending indefinitely to positive infinity.
Writing the Interval Notation Therefore, the interval notation for the set is ( 2 , ∞ ) . The parenthesis '(' indicates that 2 is not included, and the infinity symbol ∞ indicates that the interval extends indefinitely to the right.
Examples
Interval notation is used in various fields, such as calculus and real analysis, to represent sets of real numbers. For example, when describing the domain or range of a function, interval notation provides a concise way to specify the set of possible input or output values. Consider the function f ( x ) = x − 1 . The domain of this function, the set of all possible x values for which the function is defined, can be expressed in interval notation as [ 1 , ∞ ) , indicating that x can be any real number greater than or equal to 1.
The set 2 \}"> { x ∣ x > 2 } in interval notation is expressed as ( 2 , ∞ ) . This notation indicates that all real numbers greater than 2 are included, while 2 itself is not part of the set. The interval extends indefinitely towards positive infinity.
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