Is there an integer which is its own additive inverse?

Answer

To determine if there is an integer that is its own additive inverse, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Additive Inverse**:
- The additive inverse of a number \( A \) is another number \( B \) such that when you add \( A \) and \( B \), the result is the additive identity, which is 0.
- Mathematically, this can be expressed as:
\[ A + B = 0 \]

2. **Identify the Additive Identity**:
- The additive identity is 0. This means that adding 0 to any number does not change the value of that number.

3. **Check if an Integer can be its Own Additive Inverse**:
- We need to find an integer \( A \) such that:
\[ A + A = 0 \]
- This simplifies to:
\[ 2A = 0 \]

4. **Solve for A**:
- To find \( A \), we can divide both sides of the equation by 2:
\[ A = 0 \]

5. **Conclusion**:
- The only integer that satisfies the condition of being its own additive inverse is 0. Therefore, the answer is:
- Yes, the integer 0 is its own additive inverse.