How will I write (infinity, -2/3) u (2, infinity ) in set builder notation

To write the union of the intervals \((-\infty, -\frac{2}{3}) \cup (2, \infty)\) in set builder notation, you express the set as the collection of all real numbers \(x\) that satisfy the conditions defined by the intervals.

In set builder notation, this would be written as:

\[
\{ x \in \mathbb{R} \mid x < -\frac{2}{3} \text{ or } x > 2 \}
\]

This means the set of all \(x\) in the real numbers such that \(x\) is either less than \(-\frac{2}{3}\) or greater than 2.

Would you like more details or have any questions? 

Here are five related questions for further exploration:

1. How do you write the intersection of two intervals in set builder notation?
2. What is the difference between interval notation and set builder notation?
3. How do you express a set that includes its endpoints (closed intervals) in set builder notation?
4. Can set builder notation represent sets that are not intervals?
5. How do you write a union of more than two intervals in set builder notation?

**Tip:** In set builder notation, always ensure to clearly specify the variable and the condition it must satisfy within the set.

Learn how to write the union of intervals (-∞, -2/3) ∪ (2, ∞) in set builder notation. Understand the concept of set builder notation and its application to interval notation. Suitable for high school and above.

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