the set of all integre multiples of 3 that are greater than zero

The set of all integer multiples of 3 that are greater than zero can be represented as:

\[
S = \{ 3, 6, 9, 12, 15, 18, \dots \}
\]

This set contains all positive integers of the form \( 3n \), where \( n \) is a positive integer (\( n \in \mathbb{Z}^+ \)).

**In mathematical notation:**

\[
S = \{ 3n \mid n \in \mathbb{Z}^+ \}
\]

This means that every element of the set is a multiple of 3, and \( n \) is any positive integer, ensuring that the multiples are greater than zero.

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Here are 5 related questions for further exploration:

1. How would you describe the set of integer multiples of 5 greater than zero?
2. What is the set of all negative integer multiples of 3?
3. How would you find the sum of the first \( n \) multiples of 3?
4. What is the set of all integer multiples of 3 less than 100?
5. How can we express the set of all multiples of a number \( k \)?

**Tip:** When working with sets of multiples, you can always express them as \( k \times n \), where \( n \) is an integer and \( k \) is the number whose multiples you're considering.

The set of all integer multiples of 3 that are greater than zero

Discover how to represent the set of all positive integer multiples of 3 using set theory. This problem demonstrates how to express multiples of 3 in a mathematical form and introduces basic number theory concepts. Ideal for students in Grades 6-8.

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