Successor of a 3-digit number is always a 3-digit number.
Step 1: “Successor” means the next number. If a number is \(n\), its successor is:
\(\text{successor}(n) = n + 1\)
Step 2: A 3-digit number is any number from:
\(100 \le n \le 999\)
Step 3: For many 3-digit numbers, adding 1 keeps it 3-digit. Example:
\(350 + 1 = 351\)
Step 4 (Important counterexample): Take the largest 3-digit number:
\(999\)
Its successor is:
\(999 + 1 = 1000\)
\(1000\) is a 4-digit number.
Conclusion: Because there exists a 3-digit number (\(999\)) whose successor is not 3-digit, the statement “always a 3-digit number” is false.