Transfinite sets: limits of knowledge
The paper considers semantic problems of the study of infinite sets. It shows that there exist various ideas about substantial foundation, basic notions and the structure of infinite sets; these ideas result in various and contrary conclusions. So, in this field, due to limited capacities of the substance of the human mind there are certain limits of knowledge. Therefore different ideas, arguments and conclusions have a right to coexist equally, like Bohr principle of complementarity in physics.