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The English mathematician and philosopher Bertrand Russell
More difficult to overlook, however, are facts to which the English mathematician and philosopher Bertrand Russell - https://domyhomework.club/analogy-homework/ (1872 to 1970) drew attention as early as 1901 and which lead to the contradictions known as Russell'S antinomies (also known as one of the antinomies or paradoxes of set theory).
Russell gave as an example the set M of all sets that do not contain themselves as an element. What then can be said about M itself?
If one assumes that M contains itself as an element, then M (as an element of M!) belongs to those sets that do not contain themselves as an element - math xl answers - in contradiction to the assumption.
If, on the other hand, one assumes that M does not contain itself as an element, then M must, according to definition, belong to M. In both cases, a contradiction arises - the formation of the set M in the way shown is inadmissible.
For this incorrect definition of the set as "set of all sets ...", there are numerous illustrative dressings, all of which ultimately lead to a contradiction - https://domyhomework.club/ . The best-known example might be the set of all men of a certain village who do not shave themselves but are shaved by the village barber. Here, too, it is not possible to decide where the village barber himself belongs.
Contradictions can arise when objects of a basic area are grouped into sets that are themselves only defined by this formation of sets. It must be possible to imagine the objects to be combined as existing before the formation of the set.
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