The most reasonable set of numbers to describe a person's hat size is whole numbers.
Hat sizes are typically whole numbers (like 7, 7.5, etc. in some systems, but often rounded to the nearest whole number for general sizing). Whole numbers do not include fractions or decimals, which makes them appropriate for most common hat sizing systems.
Rational numbers could also be considered, as hat sizes can include decimals (like 7.5), but whole numbers are the most straightforward representation in typical sizing systems.
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