We present the cosmic neutrino detecting potential of the Telescope Array for quasihorizontally downward and upward air showers initiated by very high energy neutrinos penetrating the air and the Earth respectively. We adopted model predictions for extraterrestrial neutrino fluxes from active galactic nuclei, gamma-ray bursts, Greisen photo production, the collapse of topological defects, and Z-bursts. The Telescope Array, using a large array of bright and wide field-of-view fluorescence telescopes, can explore these very high energy cosmic neutrino sources.

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