George cantor. infinite numbers - Essay Example

Cantor 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 specialized in mathematics and physics and this institution gave him the chance to interact with great mathematicians such as Weierstrass and Kronecker bringing him closer to his career as a mathematician (Putnam, 12). After graduating from the university, he ended up becoming an unpaid lecturer since he could not secure himself a stable employment.

In 1874, he got a position as an assistant professor at the University of Halle. It is in this same year that he married. His intensive research and analysis in mathematics had not ended yet and it is during this same year that he published his first article on set theory. In his research on set theory, Cantor dug deep into the foundations of infinite sets, which interested him most. He published 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 provisions 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 Gauss’s argument saying that sets are complete number of members. In fact, Cantor went ahead and termed infinite numbers to be transfinite and as a result came up with completely new discoveries (Joseph, 188). Such discoveries saw him promoted to be the professor in 1879. Kronecker opposed Cantor’s 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 Cantor’s argument and responded to Kronecker proving to him that Cantor was actually right. Kronecker’s opposition did not stop or delay Cantor’s 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 operation of set theory. He provided that if X and Y are unique sets 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, making it the most prominent and his greatest contribution to mathematics. Following this provision, Cantor’s work and contribution in mathematics went down and almost ceased.