The most reasonable set of numbers to describe a person's hat size would be whole numbers. Hat sizes are typically measured in whole numbers (e.g., size 7, size 8), and while they can sometimes include half sizes (e.g., size 7.5), the measurement remains a finite set of values rather than encompassing fractions or irrational numbers.
However, if we consider sizes that include those halves, rational numbers could also be a reasonable option, as they include both whole numbers and fractions. That said, for the most common classifications, whole numbers are most appropriate.