What is the traditional mathematical term for a value of zero?

The traditional mathematical term for a value of zero is indeed zero itself. In mathematics, zero is a fundamental concept that represents a null quantity or a state of having no value. It serves as a placeholder in our number system and is crucial in various mathematical operations, such as addition and subtraction. It is also the identity element for addition, meaning that adding zero to any number does not change the value of that number.

The other terms listed, while they may convey a similar sense of lack or absence in informal contexts, do not specifically encapsulate the established mathematical definition of zero. For example, "null" is often used in computer science and logic, and it does not carry the same connotations as the established mathematical term. "Empty" and "nothing" are more qualitative descriptors rather than definitive numerical terms. Therefore, zero stands alone as the precise and universally recognized term in mathematics for the value of zero.