Russells paradox

is as follows: Consider a set V that co ntains all (and only those) sets X such that X is not an element X should demand now the question - whether V is an element of V? If so, then V does not satisfy the property elements of the set V , so there is an element of V. If we assume that V is not part of V, then (by definition V) V must be an element of V. In this way we arrive at the contradiction . The contradiction was pointed out Bertrand Russell in 1901. It was a big blow to people in developing set-theoretical foundations of mathematics, who until then had been received that all mathematical objects are collections.