set theory, it was a mathematical concept that used to tell what a set is, George Cantor's "Set Theory" and "The Number Game"

 'set theory', it was a mathematical concept that used to tell what a set is,

 George Cantor's "Set Theory" and "The Number Game"

 In school time we were taught 'set theory', it was a mathematical concept that used to tell what a set is, who would say a subset, for example, if there were fifty children in a group, we would say it was fifty children.  Is the set of  The theory starts with such simple examples but becomes so complex that the brain stops shaking.  The inventor of this theory was German mathematician George Cantor.  Canter proved that the largest 'cardinal number' is not something that cannot be found.  A number is a real number that provides the answer to a question.  For example, if we count a passenger on a bus and the answer is twenty, then 20 would be called real.  On the contrary, if you start counting the vehicles passing by the Motorway Tool Plaza at six o'clock in the morning that this is the first car, this is the second and this third you will say one, two, three, four, five - and this is normal.  According to Kantor's theory, a set of real numbers can be created, this set can be limited and unlimited.  For example, the set of natural and real numbers will be called unlimited.  Canter proved that sets of real numbers have higher numbers than natural numbers.  For those who do not know the difference between natural and real numbers, it is enough to know that one, two, three, four, five, six etc. are called natural numbers, whereas in addition to the natural numbers, the negative one, the negative two,  Negative three are also included.  As we can say, the set of natural numbers is a subset of real numbers.  This was the first proof of the actual numbers that Cantor presented.  The second proof was that not every natural

number can be 'numbered' by the real number.  That means we can have one instead of one, two against two, three against three, but the real numbers cannot be negative one, negative two, or natural number one, two or three, than negative three.  This also proves that the real numbers are in the "majority" rather than the natural numbers.  Canter did not end the matter here, but one step further, he added that any set had a smaller number than its 'strength'.  That is, if a set contains 'x' numbers, then a subset of 2 x will always have more numbers than that.  Thus, Cantor proved that a number can never be the greatest cardinal number because if we do not pick the largest number, its 'powerful' set will always be greater than that.

 George Cantor Kate doesn't know, but I must have been sweating under my teeth while writing.  Cantor's theory is more philosophical than mathematical.  It seems to me that to some extent it is in harmony with God's concept.  Just as the infinite limit of God cannot be heard in our mind, so much of the real prime cannot even be imagined because it is impossible to attain it, we cannot do anything to cover its greatness, to test it on some measure of the material world.  Well, why should we not take our thinking imaginatively into an infinite space and time, that 'prime minister' will still be outside that concept.  Bertrand Russell's theory of this set of canters was fascinating, and he felt that there was something wrong with this theory.  , And there is no greater number because every possible item is already there and nothing is left and yet, even if, say, Cantor, that number is not considered to be the real prime, a contradiction will be created.  Must have  Russell did not have a solution to this contradiction, so in the beginning, the four naysayers accepted this theory.  Russell writes: "So you know that not all the goods in the world are as high in rank as the items that can be sorted ...  So all the goods in the world are not more than the prime number in any way.  As you now know from mathematics, the definitive and absolute proof of this is that there is no such thing as total mixing in the heavens and the earth, as we can imagine on the basis of our philosophy. "  At the time of the dialogue hurt that "there are more things in heaven and earth, than Horatio, than dream in your philosophy".  That is to say, Russell has no limits to philosophy.  Russell later discovered the solution to the contradiction in Cantor's set theory.  Russell said that different degrees of goods are not actually goods, that is, when we say that there are men in that category, they do not become 'men' themselves, they are merely a 'logical idea' that has no concrete existence.  So when we start an infinite series of things while categorizing goods, then that is just imaginary logic.  From here Russell also laid the foundation of what he calls the 'Russell Paradox'.  Why not, I think Russell was convinced that Cantor's theory was against his philosophy, so it was Russell's compulsion to reject it.  By the way, Cantor also realized later that there was a contradiction in his theory and expressed this in his letters.  Interestingly, in Russell's response, another mathematician, Kurt Goodall, said that the reason that Russell was merely saying logical ideas was as much the reason for believing in the existence of material goods in this world.  Apparently Godel was not an atheist and believed in life after death.

 You may be wondering why I wrote this column?  What did I need to 'teach' you set theory?  If the numbers were to be written about, what would be the number of the government and the opposition?  Who is powerful?  Whose set is strong?  The implication in this regard is that the slave is absolutely indifferent to these matters.  Anyway, writing on topics that matter more than I do.  I can only tell you that George Cantor's set theory does not only apply to the post-metaphysical world but can also be applied to Pakistan.  Here you create a set of powerful people, more powerful people in that set, and then make one more set and move on, even then all these sets will not be bigger than the powerful set towards which  It was hinted at. Knowing too little, the 'mentor' did not allow me to say more than that.

 Note: The information in this column is an article by British philosopher and author 'Ray Monk' Cabertrand Russell.

 (This column was published in the Daily War today, March 7).

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