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created by changing Euclid's fifth postulate. These geometries do not lead to any internal contradictions, although, in such geometries, the sum of the angles of a triangle is different from 180°. In other words, the property "the sum of the angles of a triangle equals 180°" can be either true or false, depending on whether Euclid's fifth postulate is assumed or denied. Similarly, in the 19th century, the use of some "evident" basic properties of sets led to the contradiction of Russell's paradox.

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