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The classical Nagumo uniqueness theorem is a best possible result in the sense that if the Nagumo constant is replaced by a number greater than one then the result is false. This classical result uses the continuity of the right-hand side,/(3C, y), of the first order ordinary differential equation, and there is no explicit connection shown between the constant and the continuity of /; the observation that one makes is that the counterexample originally given by Perron uses a discontinuity atdoi:10.1090/s0002-9939-1971-0288331-1 fatcat:v4rjbknvirhdlnbs6lmt7bnbzq