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We have calculated the number of dormant, nearly isotropic Oort cloud comets in the solar system by (i) combining orbital distribution models with statistical models of dormant comet discoveries by well-defined surveys and (ii) comparing the model results to observations of a population of dormant comets. Dynamical models that assume that comets are not destroyed predict that we should have discovered approximately 100 times more dormant nearly isotropic comets than are actually seen. Thus, as comets evolve inward from the Oort cloud, the majority of them must physically disrupt.