The notation you’ve provided represents a union operation between two sets. Let’s break it down and simplify.

### Step 1: Understanding the Sets
1. **Set 1**: \((-3, 5)\)  
   The interval \((-3, 5)\) is an open interval, which means it includes all real numbers between \(-3\) and \(5\), but does not include the endpoints \(-3\) and \(5\).

2. **Set 2**: \(\{-4, -1, 0, 2, 4, 5, 6, 7, 8, 9\}\)  
   This is a discrete set that consists of specific integer elements.

### Step 2: Union of Sets
The union of these sets, \((-3, 5) \cup \{-4, -1, 0, 2, 4, 5, 6, 7, 8, 9\}\), will include:
- All elements from the interval \((-3, 5)\), which includes all real numbers from slightly greater than \(-3\) to slightly less than \(5\).
- All specific integers in Set 2.

### Step 3: Putting It Together
Now we combine them into a single set that represents all unique elements within the union:

\[
(-3, 5) \cup \{-4, -1, 0, 2, 4, 5, 6, 7, 8, 9\} = (-3, 5) \cup \{5, 6, 7, 8, 9\}
\]

So, the union simplifies to:

\[
(-3, 5) \cup \{5, 6, 7, 8, 9\}
\]

This is your final representation of the union of these two sets.

Would you like further details or explanations on any step?

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1. What is the difference between open and closed intervals?
2. How does union differ from intersection in set theory?
3. Can we represent this union on a number line?
4. How do we handle intervals when they overlap with discrete sets?
5. What are some applications of union and intersection in real-world problems?

**Tip:** In set notation, always verify if intervals are open, closed, or half-open to ensure accuracy in representation.

Explore the union of an open interval (-3,5) with a discrete set of integers {-3,-1,0,2,4,5,6,7,8,9}. This problem covers essential concepts in set theory, including union and interval notation, with a step-by-step breakdown suitable for Grades 9-11.

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