0!=0

Answer

To determine whether the statement "0! = 0" is true or false, we need to understand the definition of factorial, particularly for the case of zero.

### Step-by-Step Solution:

1. **Understanding Factorial**:
The factorial of a non-negative integer \( n \), denoted as \( n! \), is the product of all positive integers up to \( n \). For example:
- \( 3! = 3 \times 2 \times 1 = 6 \)
- \( 2! = 2 \times 1 = 2 \)
- \( 1! = 1 \)

2. **Defining Zero Factorial**:
By definition, the factorial of zero, \( 0! \), is defined to be equal to 1. This is a convention in mathematics that helps maintain consistency in various formulas, particularly in combinatorics.

3. **Mathematical Justification**:
The reason \( 0! = 1 \) can be understood through the concept of permutations. The number of ways to arrange zero objects is exactly one way: doing nothing. Therefore, \( 0! = 1 \).

4. **Conclusion**:
Since \( 0! = 1 \), we can conclude that the statement "0! = 0" is false.

### Final Answer:
The statement "0! = 0" is **false** because \( 0! = 1 \).

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