State which of the following sets are finite and which are infinite:
A=`{x:x epsilon Z" and "x gt -10}`

Answer

To determine whether the set \( A = \{ x : x \in \mathbb{Z} \text{ and } x > -10 \} \) is finite or infinite, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Set Definition**: The set \( A \) is defined to include all integers \( x \) such that \( x \) is greater than \(-10\). This means we are looking for integers starting from \(-9\) and going upwards.

2. **Identify the Elements of the Set**: The integers that satisfy the condition \( x > -10 \) are:
- \(-9\)
- \(-8\)
- \(-7\)
- \(-6\)
- \(-5\)
- \(-4\)
- \(-3\)
- \(-2\)
- \(-1\)
- \(0\)
- \(1\)
- \(2\)
- \(3\)
- \(4\)
- \(5\)
- \(6\)
- \(7\)
- \(8\)
- \(9\)
- \(10\)
- ... and so on.

3. **Determine the Nature of the Set**: Since the integers continue indefinitely in the positive direction (i.e., there is no upper limit), the set \( A \) does not have a maximum number. Therefore, it includes an infinite number of integers.

4. **Conclusion**: The set \( A \) is infinite because it contains an unbounded number of integers greater than \(-10\).

### Final Answer:
The set \( A = \{ x : x \in \mathbb{Z} \text{ and } x > -10 \} \) is **infinite**.