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Is the definition in mathematics necessarily correct?
The definition is artificially set, and the default is the linguistic description of the fact. It's like the premise of something. It is the beginning and foundation of everything in its system. Because of its artificial characteristics, the definition must be correct (note: saying it is correct does not mean admitting that it conforms to reality. Just like the definition of the intersection of two parallel lines in non-Euclidean geometry, the default is correct, but it is not realistic).

So can the definition be proved? Obviously not. Proof is to explain the process of advanced application with basic theory, and to explain the complex process with simplicity. Since definition is the basis of everything, it means that it can never be proved, and it can only be used to prove something else. (Note: Mathematician Godel's Incompleteness Theorem: In any axiomatic formal system, such as modern mathematics, on the basis of defining the axioms of the system, there are always problems that can neither be proved nor falsified. )