State whether each of the following sets is a finite set or an infinite set:
The set of integers less that 10.

Answer

To determine whether the set of integers less than 10 is a finite set or an infinite set, we can follow these steps:

### Step 1: Define the Set
We need to define the set of integers that are less than 10. This means we are looking for all integers that are smaller than 10.

### Step 2: Identify the Elements
The integers less than 10 include:
- Positive integers: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0
- Negative integers: -1, -2, -3, -4, -5, -6, -7, -8, -9, -10, and so on.

### Step 3: Analyze the Set
We see that while we can list the positive integers down to 0, the negative integers continue indefinitely. There is no limit to how far we can go into the negative integers.

### Step 4: Conclusion
Since the set of integers less than 10 includes an infinite number of negative integers, we conclude that this set is an infinite set.

### Final Answer
The set of integers less than 10 is an infinite set.

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