The expression \( u = \{x : x \in \mathbb{N}, x < 25 \} \) defines a set of natural numbers \( x \) such that \( x \) belongs to the set of natural numbers (denoted by \( \mathbb{N} \)) and \( x \) is less than 25. 

So, the set \( u \) contains all natural numbers less than 25. Since natural numbers are the set of positive integers starting from 1, the set \( u \) is:

\[
u = \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24 \}
\]

In other words, \( u \) is the set of natural numbers from 1 to 24, inclusive.

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### Related Questions:
1. What is the set of natural numbers?
2. How do we represent intervals or conditions for sets of numbers?
3. What is the difference between natural numbers and whole numbers?
4. How would the set change if \( x \in \mathbb{Z} \) instead of \( x \in \mathbb{N} \)?
5. How do we handle infinite sets of numbers?

### Tip:
In set-builder notation, the colon (:) or vertical bar (|) is often used to mean "such that," and the expression after it defines the condition elements must satisfy.

Explore how to define a set of natural numbers less than 25 using set-builder notation. This example walks through the concept of set theory and the definition of natural numbers. Ideal for students in Grades 6-8.

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