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The set described in the problem is the set of all positive integer multiples of 7. To represent this in set-builder notation using \( n \) as the variable, we want to express this set as:

\[
M = \{ n \in \mathbb{Z} \mid n = 7k, \, k \in \mathbb{Z}^+, \, k > 0 \}
\]

This notation means that \( M \) contains all integers \( n \) such that \( n \) is equal to \( 7k \), where \( k \) is a positive integer greater than zero.

Do you have any questions about set-builder notation or want more details on how it works?

Here are 5 related questions to explore:
1. What is set-builder notation and when is it used?
2. How would you express the set of multiples of any other integer, like 5 or 3, using set-builder notation?
3. Can you express negative multiples of a number using set-builder notation?
4. How would you represent the set of even numbers using set-builder notation?
5. What is the difference between set-builder and roster notation?

**Tip:** Always ensure that the constraints of your set-builder notation accurately reflect the properties of the numbers you're trying to represent (e.g., positive, greater than zero).

Represent the set with set builder notation. Use n as your variable. The set of all integer multiples of 7 that are greater than zero.

Learn how to represent the set of all integer multiples of 7 that are greater than zero using set builder notation. Explore key concepts in set theory and number theory. Suitable for Grades 7-10.

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