Georg Ferdinand Ludwig Philipp Singer He was born on March 3, 1845 in St.Petesburg, Russia, and died on January 6, 1918 in Halle, Germany. He founded set theory and introduced the concept of infinite numbers with his discovery of cardinal numbers. He also advanced the study of trigonometric series. Singer attended the University of Zurich for a time in 1862, however went to the University of Berlin where he attended conferences from Weierstrass, Kummer and Kronecker. He received his doctorate in 1867 from Berlin and accepted a position at Halle University in 1869, where he remained until his retirement in 1913. In 1885 he built a house on Händelstrasse.
OIts early documents (1870-1872) showed the influence of Weierstrass's teaching dealing with trigonometric series. In 1872 he defined irrational numbers in terms of convergent sequences of rational numbers. In 1873 he proved the accounting of rational numbers, showing that they can be matched 1-1 with natural numbers.
UA transcendental number is an irrational number that is not a root of any polynomial equation with integer coefficients. Liouville established in 1851 that transcendental numbers exist. Twenty years later Cantor showed that in a sense "almost all" numbers are transcendental.
O Cantor's next account of his work on transfinite set theory was his definition of continuity. Cantor's work was attacked by many mathematicians, an attack that was conducted by Cantor's own teacher Kronecker. Cantor never doubted the absolute truth of his work despite the discovery of the paradoxes of set theory. He was supported by Dedekind, Weierstrass and Hilbert, Russell and Zermelo. Hilbert described Cantor's work as:
the best product of mathematical genius and one of the supreme achievements of purely intellectual human activity.
UA major event planned at Halle to mark Cantor's 70th birthday in 1915 had to be canceled because of the war. Cantor was given an honorary degree from St Andrews University in 1911. He died at a psychiatric clinic in Halle in 1918.