In Roman numerals, the number 4 is correctly represented as "IV" and not "IIII". The reason for this is based on the principles of Roman numerals and their method of counting:
When forming numbers, Romans used a subtractive principle. For example, "IV" means 5 minus 1, or 4. The use of "IIII" to represent four would imply a misapplication of the rules for Roman numerals, where the same letter cannot be repeated more than three times in sequence within a numeral. Instead, the next digit in the sequence is reduced by one to form the desired number.
Here's how it applies generally:
This pattern continues for larger numbers as well, maintaining the rule that one cannot have more than three consecutive identical symbols, and the subtractive principle is used when necessary to form numbers efficiently.