Georg Cantor :: essays research papers

Georg CantorI. Georg CantorGeorg Cantor founded set theory and introduced the concept of infinite poemwith his discovery of cardinal numbers. He also advanced the teach 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 stratums until thefathers sickly health 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 hisson into the more profitable but less ch in onlyenging field of engineering. Georgwas not at all happy about this idea but he lacked the courage to stand up tohis father and relented. However, after several years of training, he became so ply up with the idea that he mustered up the courage to beg his father to becomea mathematician. Finally, just bef ore 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 on a lower floorsome 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 ready as an unpaid lecturerand later as an assistant 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 even num bers, 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 as pi(3.14159) and e(2.71828) that can never be the solution to anyalgebraic equation, were much bigger than the number of integers. Before inmathematics, infinity had been a sacred subject. Previously, Gauss had statedthat infinity should only be used as a way of mouth and not as a mathematical