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Considering Earth's potential as 0 is nothing but an assumption.We assume that Earth  is a collection of infinte negative charge and it can even supply more charges to it.As earth has such a huge amount of negative charge with capacity to be supplied with even more any other body will  be positive w.r.t Earth.Hence we assume its potential to be zero.

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As Earth can store unlimited charge its capacitance is infinity

Q=CV

=>C=Q/V

As C is infinity V has to be 0.

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