Question
Write the set \( \{x \mid x>4\} \) in interval notation
Ask by Rose Garza. in the United States
Feb 04,2025
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Answer
The set \( \{x \mid x > 4\} \) in interval notation is \( (4, \infty) \).
Solution
The set \( \{x \mid x > 4\} \) consists of all real numbers greater than 4. In interval notation, this set is represented as:
\[
(4, \infty)
\]
**Explanation:**
- **Parentheses \((\,)\):** Indicate that the endpoint is **not** included in the interval. Since the inequality is \( x > 4 \) (and not \( x \geq 4 \)), we use a parenthesis at 4.
- **Infinity \(\infty\):** Represents that the interval extends indefinitely in the positive direction. Note that infinity is always denoted with a parenthesis because it is not a real number and cannot be included in the set.
**Complete Interval Notation:**
\[
(4, \infty)
\]
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Simplify this solution The Deep Dive
The set \( \{x \mid x>4\} \) can be expressed in interval notation as \( (4, \infty) \). This notation indicates that the set includes all numbers greater than 4, extending infinitely in the positive direction, but does not include 4 itself. In interval notation, parentheses are used to denote that the endpoints are not included in the set, which is why we see \( (4 \) rather than \( [4 \). It’s a simple yet efficient way to capture ranges of values!
