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03/30/2022 at 4:49 AM #82147
31253819ParticipantThe most important basic concepts in mathematics
Last edited: 30.03.2022 04:54
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 – domyhomework – in contradiction to the assumption.
If, on the other hand, we assume that M does not contain itself as an element, then M must belong to M according to the definition. 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 – math xl answers . The bestknown 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. One must be able to imagine the objects to be combined as existing before the formation of the set.
One therefore demands:
Sets may only contain elements of the next smaller “level”, whereby the elements of sets of the 1st level are “individuals”, i.e. individual objects of reality or of our thinking, of our conceptions; sets of the 2nd level are created by combining sets of the 1st level as elements, and so on.
The set N thus contains as elements the numbers 0, 1, 2, 3, …; the set B of certain number ranges could include as elements, for example, the set N , the set Zn of the negative integers, the set Qg of the fractional – analogy helper , noninteger numbers, and so on.
A way out of the contradictions revealed by Russell was the axiomatisation of set theory. In 1908, Ernest Zermelo (1871 to 1953) gave an axiom system for set theory, which was itself, however, the subject of controversial discussions.
Read also:
Galileo Galilei and the Church
Leonardo da Vinci: Fantastic machines and buildings
The composition of CocaCola
The influence of Erasmus of Rotterdam on other personalities
Construction of the continuous division 
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07/27/2022 at 8:21 AM #95543
Lilly MarkParticipantUnits are, in my opinion, the key idea in mathematics. In general, we deal with a certain quantity of items every day, such as money, food, petrol, space, and time. These can all be divided into smaller components. The only computations performed on these units are addition, subtraction, and multiplication. Regards: Nursing Essay Writing Service
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08/06/2022 at 2:45 PM #97244
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09/01/2022 at 10:53 AM #101429
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