Which of the following statements is INCORRECT with respect to the natural numbers ?

Options

A. Every natural number has a successor.
B. Every natural number has a predecessor.
C. Division by zero is not defined.
D. All whole numbers are not natural numbers.

Answer

To determine which statement is INCORRECT with respect to natural numbers, we need to analyze the properties of natural numbers.

### Step-by-Step Solution:

1. **Understand Natural Numbers**:
- Natural numbers are defined as the set of positive integers starting from 1 and going to infinity.
- Examples of natural numbers: 1, 2, 3, 4, 5, ...

**Hint**: Remember that natural numbers do not include zero or negative numbers.

2. **Evaluate the Statements**:
- We need to evaluate the statements given in the question to see which one is incorrect.

3. **Statement 1**: "Every natural number has a successor."
- The successor of a natural number \( n \) is \( n + 1 \).
- For example, the successor of 1 is 2, the successor of 2 is 3, and so on.
- Therefore, this statement is **correct**.

**Hint**: Think about what happens when you add 1 to any natural number.

4. **Statement 2**: "Every natural number has a predecessor."
- The predecessor of a natural number \( n \) is \( n - 1 \).
- For example, the predecessor of 2 is 1, the predecessor of 3 is 2, but the predecessor of 1 is 0.
- Since 0 is not a natural number, this statement is **incorrect**.

**Hint**: Consider what happens when you try to find the predecessor of the smallest natural number.

5. **Conclusion**:
- The statement that is INCORRECT with respect to natural numbers is: "Every natural number has a predecessor."

**Final Answer**: The incorrect statement is: "Every natural number has a predecessor."