Define Finite and Infinite Sets – Definition, Examples & Activity (Class 6 Maths)

Unit 1 – Sets

Define Finite and Infinite Sets (With Examples & Activity)

In mathematics, a set is a well-defined collection of objects, numbers, or symbols. In this lesson, we will understand two important types of sets:

• Finite Sets
• Infinite Sets

📘 Examples of Sets

Consider the following sets:

• A = {2, 4, 6}
• B = {1, 2, 3, …}
• C = {6, 4, 2}
• D = {x, y, z}
• E = {1, 3, 5, 7, …}
• F = {5, 10, 15, 20, 25, …}

🔹 Finite Set

Look at Set A = {2, 4, 6}

This set has only three elements. Since the number of elements is limited, it is called a finite set.

✅ Definition:

A set which has a limited number of elements is called a finite set.

Examples of Finite Sets:

• A = {2, 4, 6}
• C = {6, 4, 2}
• D = {x, y, z}

All these sets have a fixed and countable number of elements.

🔹 Infinite Set

Now consider Set B = {1, 2, 3, …}

This set continues forever. The elements never end. Therefore, it is an infinite set.

✅ Definition:

A set which has an unlimited number of elements is called an infinite set.

Examples of Infinite Sets:

• B = {1, 2, 3, …}
• E = {1, 3, 5, 7, …} (Odd numbers)
• F = {5, 10, 15, 20, 25, …} (Multiples of 5)

📝 Activity: Identify Finite and Infinite Sets

Tick (✓) the finite sets and cross (✗) the infinite sets.

1. Set of all citizens of Pakistan → ✓ Finite
2. Set of all whole numbers less than 9999 → ✓ Finite
3. Set of drops of water in a river → ✓ Finite (very large but limited)
4. The set of all letters of the English alphabet → ✓ Finite
5. {1, 2, 3, …} → ✗ Infinite
6. {d, o, r} → ✓ Finite
7. {2, 4, 6, …} → ✗ Infinite

🎯 Key Difference Between Finite and Infinite Sets

📌 Conclusion

• If a set has a fixed number of elements, it is finite.
• If a set continues endlessly, it is an infinite set.

Understanding finite and infinite sets is the foundation of set theory and helps in learning advanced mathematical concepts.

• Types of Sets

• Natural Numbers

• Set Theory Basics