George cantor. infinite numbers Essay Example | Topics and Well Written Essays - 1000 words

George cantor. infinite numbers - Essay Example precentor had the passion of becoming a mathematician and in 1862 he joined University of Zurich (Putnam, 10). Cantor later moved to the University of Berlin following the death of his father. Here, he vary in mathematics and physics and this institution gave him the chance to interact with great mathematicians such as Weierstrass and Kronecker livery him closer to his career as a mathematician (Putnam, 12). After graduating from the university, he ended up becoming an non-paying lecturer since he could non secure himself a stable employment. In 1874, he got a put down as an assistant professor at the University of Halle. It is in this same year that he married. His intensive seek and analysis in mathematics had not ended yet and it is during this same year that he make his first article on circuit hypothesis. In his research on set theory, Cantor dig deep into the foundations of infinite sets, which interested him most. He pu blished a number of papers on set theory between 1874 and 1897 and come to the end of 1897 he was in a position to prove that integers in a set contained equal number of members to those contained in cubes, squares and numbers. He also provided that the counts/numbers in a line which is infinite needs to be equal to the points in a line segment in addition to his earlier statement that values which cannot be used as solutions to algebraic equations such as 2.71828 and 3.14159 in transcendental numbers will be extremely bigger than their integers. Before these readinesss by him, the subject of infinity used to be treated as revered. Such a view had been propagated by mathematicians such as Gauss who provided that infinity should only be used for speaking purposes as opposed to being used as mathematical values. However, Cantor opposed Gausss argument saying that sets are breeze through number of members. In fact, Cantor went ahead and termed infinite numbers to be transfinite and as a impression came up with completely new discoveries (Joseph, 188). Such discoveries saw him promoted to be the professor in 1879. Kronecker opposed Cantors argument on the basis that only real numbers may be termed to be integers terming decimals and fractions as irrational with the interpretation that they were not elements of consideration in mathematics business. However, some other mathematicians such as Richard Dedekind and Weierstrass supported Cantors argument and responded to Kronecker proving to him that Cantor was actually right. Kroneckers opposition did not stop or delay Cantors work and in 1885, he extended his theory of order types and cardinal numbers in such a way that his previous theory on ordinal numbers gained some special importance. The extension was followed by the article he published in 1897 that marked his final treat to the theory of sets. As a conclusion, Cantor elaborated on the accomplishment of set theory. He provided that if X and Y are unique s ets which are equivalent to a subset of Y and Y is equivalent to a subset, say subset X, then X and Y must be equivalent. This provision on set theory received great support from many mathematicians such as Schrat and Bernstein, reservation it the most prominent and his greatest contribution to mathematics. Following this provision, Cantors work and contribution in mathematics went down and almost ceased.