Georg Cantor
Georg Cantor
I. Georg Cantor
Georg Cantor founded set theory and introduced the concept of infinite numbers with his discovery of cardinal numbers. He also advanced the study of trigonometric series and was the first to prove the nondenumerability of the real numbers. Georg Ferdinand Ludwig Philipp Cantor was born in St. Petersburg,
Russia, on March 3, 1845. His family stayed in Russia for eleven years until the father's sickly health forced them to move to the more acceptable environment of
Frankfurt, 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 son into the more profitable but less challenging field of engineering. Georg was not at all happy about this idea but he lacked the courage to stand up to his father and relented. However, after several years of training, he became so fed up with the idea that he mustered up the courage to beg his father to become a mathematician. Finally, just before entering college, his father let Georg study mathematics. In 1862, Georg Cantor entered the University of Zurich only to transfer the next year to the University of Berlin after his father's death.
At Berlin he studied mathematics, philosophy and physics. There he studied under some of the greatest mathematicians of the day including Kronecker and
Weierstrass. After receiving his doctorate in 1867 from Berlin, he was unable to find good employment and was forced to accept a position as an unpaid lecturer and 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 Cantor published his first paper on the theory of sets. While studying a problem in analysis, he had dug deeply into its foundations, especially sets and infinite sets. What he found baffled him. In a series of papers from 1874 to 1897, he was able to prove that the set of integers had an equal number of members as the set
of
I. Georg Cantor
Georg Cantor founded set theory and introduced the concept of infinite numbers with his discovery of cardinal numbers. He also advanced the study of trigonometric series and was the first to prove the nondenumerability of the real numbers. Georg Ferdinand Ludwig Philipp Cantor was born in St. Petersburg,
Russia, on March 3, 1845. His family stayed in Russia for eleven years until the father's sickly health forced them to move to the more acceptable environment of
Frankfurt, 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 son into the more profitable but less challenging field of engineering. Georg was not at all happy about this idea but he lacked the courage to stand up to his father and relented. However, after several years of training, he became so fed up with the idea that he mustered up the courage to beg his father to become a mathematician. Finally, just before entering college, his father let Georg study mathematics. In 1862, Georg Cantor entered the University of Zurich only to transfer the next year to the University of Berlin after his father's death.
At Berlin he studied mathematics, philosophy and physics. There he studied under some of the greatest mathematicians of the day including Kronecker and
Weierstrass. After receiving his doctorate in 1867 from Berlin, he was unable to find good employment and was forced to accept a position as an unpaid lecturer and 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 Cantor published his first paper on the theory of sets. While studying a problem in analysis, he had dug deeply into its foundations, especially sets and infinite sets. What he found baffled him. In a series of papers from 1874 to 1897, he was able to prove that the set of integers had an equal number of members as the set
of