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The fundamental function E(S, V, N) implies that one finds the value E such that S = S(E, V, N) where's on the left hand side and N and E on the right are all specified. In principle, if the entropy could be any mathematical function, there could be multiple solutions of E that could satisfy this relationship and hence the internal energy would not be a well-defined function of the entropy. Explain why in fact this is nearly never the case.

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