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Well known that mathematics and physics have problems in their development. Only one mathematician, Morris Kline, discovered illogicality of development of mathematics. Despite this, he attempted to justify illogicality in math by fruitfulness of usage of mathematics in physics, instead to stay problem about illogical development of physics. Here is discussing inconsistencies of undefined notions which are reasons of paradoxes. Main initial notion of mathematics is notion of infinity, and it has inconsistence and this inconsistency is distributed to derived notions of infinitesimal and continuity. Those notions related to almost all branches of mathematics which used physics. Also in work is considering miss inconsistencies of Euclid’s and non-Euclid’s geometries. A lot approaches like “physics is geometry or geometry is physics” was and is ignoring those inconsistencies of geometries.

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