Which of the following sets are finite or infinite?Justify.
8. The set of all the points on the circumfrence of the circle.

Answer

To determine whether the set of all points on the circumference of a circle is finite or infinite, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Circle**:
A circle is defined as the set of all points that are at a fixed distance (radius) from a central point (the center of the circle).

2. **Defining the Set**:
Let’s denote the set of all points on the circumference of a circle with radius \( r \) and center at point \( O \) as \( S \). Thus, \( S = \{ P \mid \text{distance}(P, O) = r \} \).

3. **Analyzing the Points**:
The circumference of a circle is a continuous curve. This means that between any two points on the circumference, there are infinitely many other points. For instance, between any two points \( A \) and \( B \) on the circle, you can always find another point \( C \) such that \( A \), \( C \), and \( B \) are all distinct points on the circumference.

4. **Conclusion**:
Since there are infinitely many points between any two points on the circumference, we conclude that the set \( S \) is not countable. Therefore, the set of all points on the circumference of a circle is an **infinite set**.

### Final Answer:
The set of all points on the circumference of a circle is an infinite set.

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