Georg Cantor :: essays research papers

Georg CantorI. Georg CantorGeorg Cantor founded set speculation and introduced the concept of infinite numberswith his discovery of cardinal numbers. He also advanced the paper oftrigonometric series and was the first to prove the nondenumerability of thereal numbers. Georg Ferdinand Ludwig Philipp Cantor was born in St. Petersburg,Russia, on March 3, 1845. His family stayed in Russia for eleven classs until thefathers sickly wellness forced them to move to the more acceptable environment ofFrankfurt, Germany, the place where Georg would spend the rest of his life.Georg excelled in mathematics. His father saw this gift and tried to push his discussion into the more profitable but less challenging field of engineering. Georgwas not at all happy about this idea but he lacked the courageousness to stand up tohis father and relented. However, after several years of training, he became sofed up with the idea that he mustered up the courage to knock his father to becomea mathematicia n. 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 doctorate in 1867 from Berlin, he was unable tofind good employment and was forced to accept a position as an unpaid lecturerand later as an jock professor at the University of Halle in1869. In 1874,he married 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 problem 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 number of members as the setof ev en numbers, squares, cubes, and roots to equations that the number ofpoints in a line segment 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(prenominal) as pi(3.14159) and e(2.71828) that can never be the solution to anyalgebraic equation, were much larger than the number of integers. Before inmathematics, infinity had been a set apart subject. Previously, Gauss had statedthat infinity should only be used as a way of speaking and not as a mathematical