Georg Cantor :: essays research papers

Georg CantorI. Georg CantorGeorg Cantor founded solidifying possibility and introduced the concept of infinite numberswith his discovery of cardinal numbers. He excessively advanced the study oftrigonometric series and was the premiere to prove the nondenumerability of the authentic numbers. Georg Ferdinand Ludwig Philipp Cantor was born in St. Petersburg,Russia, on March 3, 1845. His family stayed in Russia for xi divisions until the aims sickly health strained them to move to the more bankable environment ofFrankfurt, Germany, the place where Georg would spend the rest of his life.Georg excelled in mathematics. His father cut this gift and tried to push hisson into the more profitable solely less ch onlyenging field of engineering. Georgwas not at all skilful about this idea but he lacked the courage to stand up tohis father and relented. However, after several years of training, he became so cater up with the idea that he mustered up the courage to beg his father to beco mea mathematician. Finally, just before entering college, his father let Georgstudy mathematics. In 1862, Georg Cantor entered the University of Zurich onlyto transfer the next year to the University of Berlin after his fathers death.At Berlin he studied mathematics, philosophy and physics. There he studied undersome of the greatest mathematicians of the day including Kronecker andWeierstrass. After receiving his doctors degree in 1867 from Berlin, he was unable tofind good employment and was forced to accept a position as an unpaid lecturerand posterior as an assistant professor at the University of Halle in1869. In 1874,he marital and had six children. It was in that same year of 1874 that Cantorpublished his first paper on the theory of sets. While studying a business inanalysis, he had dug deeply into its foundations, especially sets and infinitesets. What he found baffled him. In a series of papers from 1874 to 1897, he wasable to prove that the set of integers had an equal n umber of members as the setof even numbers, squares, cubes, and roots to equations that the number ofpoints in a line separate is equal to the number of points in an infinite line, aplane and all mathematical space and that the number of transcendental numbers,values such as pi(3.14159) and e(2.71828) that can never be the solution to anyalgebraic equation, were a lot larger than the number of integers. Before inmathematics, infinity had been a religious subject. Previously, Gauss had statedthat infinity should only be used as a way of speaking and not as a mathematical