The man who discovered different infinities-Georg Cantor

Hello Students, Welcome to our YouTube Channel The Mathematics Cantor Today we are going to talk about a Mathematician whose principles are surrounded by life-threatening controversies The name of that great Mathematician is George Cantor who was born on 3rd March 1845 in St. Petersburg which is situated in Russia His father's name was George Waldemar Cantor who was also a successful merchant George Cantor's primary education i.e. early education was done through a private tutor at home After that he studied in a primary school in St. Petersburg After that when he was 11 years old he came to Germany with his family in 1856 In 1860, Cantor studied in a real school in Darmstadt Everyone was surprised to see his extraordinary skills in Mathematics In 1862, George entered Swiss Federal Polytechnic In 1863, his father died At that time, Cantor completed his further studies from Berlin University In 1867, he got a direct qualification in the field of Mathematics He gave the principle of Set Theory which later became Fundamental Theory Set Theory which is the basis of Modern Mathematics Its usefulness can be understood from the fact that without Set Theory neither the existence of a computer nor the solving of the mysteries of the universe would have been easy Cantor also talked about the importance of 1-1 onto functions between two sets He defined Cardinality and Ordinal Cardinality of a set is the number of elements of the set If a bijective function i.e. 1-1 onto function is defined between two sets A and B then both the sets will be similar When we say this, the Cardinality of both the sets will be same He also defined Countability and Uncountability Countable is a set which can be kept in an order and it can be told that what will be the next number after one number He said that if a set is similar to the natural number set i.e. if a function is defined which is 1-1 onto between these two sets then that set will be similar to the natural number set and the elements of that set can be kept in a natural order and then that set will become countably infinite otherwise that infinite set will become uncountable From here, he got the idea that we can compare the Cardinality of an infinite set He said that we can compare the Cardinality of an infinite set Before him, all the mathematicians believed that the Cardinality of an infinite set is same and it is equal to the infinite He said that we can't think beyond the infinite So according to all these, the Cardinality of natural number set, the Cardinality of real number set, and the Cardinality of set of points on circle were all equal But Cantor challenged the power of the infinite He said that there is something beyond the infinite He named the Cardinality of natural number set as Alif Naught He said that the Cardinality of uncountable set is greater than the Cardinality of countable infinite set He gave the theory of transfinite number which was the most controversial The Cardinality of infinite set is called transfinite number Before this theory, it was believed that all the infinites are equal But he said that there are categories of infinites He named the Cardinality of real number set as Continuum He said that there is no transfinite number between Alif Naught and Continuum He proved a theory That theory was There doesn't exist a function defined from natural number to power set of natural number which is onto And then he proved that The Cardinality of power set of natural number is greater than the Cardinality of power set of natural number Then he proved that The Cardinality of power set of natural number is similar to The Cardinality of power set of all functions which is defined from natural number to the set collecting 2 points 0 and 1 Which is similar to real number Because all binary expressions are written in the form of sequence 0 and 1 And he said that The Cardinality of power set of natural number is similar to the Cardinality of real number And the Cardinality of real number is similar to the Cardinality of all sequences whose terms belongs to the set containing 0 and 1 Therefore, 2 to the power of Alif Naught is equal to Continuum And he said that The uncountable set which is not similar to the real number set Will be represented by other transfinite numbers That is Alpha, Beta and Gamma Then he gave many theorems like Alpha plus Beta, Beta plus Gamma According to Cantor, No matter how big the circle is, there will be infinite points in it That is, the number of points on it will be equal That is, the number of points in the sun, the number of points on the earth, the number of points on the tennis ball will be equal Cantor worked on functional theory and established different relations between functions The established mathematicians of that time told their discoveries beyond mathematical rules Some said that their rules are more spiritual than mathematics Some even said that he has dug the grave of mathematics On the other hand, religious gurus called his work a challenge to the power of God While the mathematician himself said that God himself has given him this knowledge of mathematics Cantor had to face a lot of opposition Another mathematician named Dedekind supported Cantor through his guru and colleague Kronikar Later, David Hilbert said about Cantor that we have no right to exclude anyone from the mathematics he has created Subsequent criticism made Cantor a victim of depression He died on January 6, 1918, which was a tragic event in the field of mathematics We should be inspired by his life and we should also create history in the field of mathematics And remember, whatever you do, it will definitely bear fruit one day Like this, you all stay on this channel, we will also tell you about all the mathematicians Thank you