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What are the mathematical meanings of those hollow letters in Berkeley Mathematics Problem Set?
If you mean that the hollow n should refer to the natural field, that is, the set of all natural numbers, R should be the real field, Q should be the rational field, and C should be the complex field. Hollow f should refer to the set of hollow r and c, which is a field.

The translation of Field should be domain (it should be called domain in mathematics, but it is called field in physics anyway. )