Give an example of an infinite and finite set.

Sure! Here is an example of both **an infinite** and **a finite** set:

### **1. Infinite Set:**
- **Set of natural numbers**: \( \mathbb{N} = \{1, 2, 3, 4, 5, \dots\} \)
  - This set is infinite because it has no end; you can always find a larger natural number.

### **2. Finite Set:**
- **Set of vowels in the English alphabet**: \( V = \{a, e, i, o, u\} \)
  - This set is finite because it contains exactly 5 elements and no more can be added.

Would you like further details or have questions? 

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Here are 5 related questions for deeper exploration:

1. What is the difference between countably infinite and uncountably infinite sets?  
2. Can a set have both finite and infinite subsets?  
3. How do we determine if a set is finite or infinite in complex cases?  
4. What are some examples of uncountable infinite sets?  
5. Are all sets with a repeating pattern infinite?

**Tip:**  
An easy way to recognize an infinite set is if you cannot list all its elements in a finite amount of time!

Explore examples of both infinite and finite sets in set theory. Learn about the set of natural numbers as an infinite set and the set of vowels in the English alphabet as a finite set. Ideal for students in Grades 6-8.

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