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The problem asks you to use set-builder notation to represent the set \( H \), defined as the set of real numbers greater than six.

In set-builder notation, we would write this as:
\[
H = \{ x \mid x > 6, \, x \in \mathbb{R} \}
\]

This reads as "H is the set of all \( x \) such that \( x \) is greater than 6, and \( x \) is a real number."

Would you like further details on set-builder notation or have any questions?

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Here are some related questions that could help deepen understanding:

1. How would you represent a set of real numbers less than a certain value in set-builder notation?
2. What does the symbol \( \mathbb{R} \) represent in mathematics?
3. How would the notation change if we included 6 in the set (i.e., \( x \geq 6 \))?
4. How could you represent an interval for all real numbers between two values, like 3 and 7?
5. How would the notation change if we were working with integers instead of real numbers?

**Tip:** In set-builder notation, the vertical bar \( | \) or colon \( : \) means "such that" and is used to define the property that elements of the set must satisfy.

Use the variable x to write the set in set-builder notation. Let H be the set of real numbers greater than six.

Learn how to represent a set of real numbers greater than six in set-builder notation. This problem covers key mathematical concepts in set theory, inequalities, and real numbers, suitable for students in Grades 9-10.

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