# The Mathematical Theory Of Georg Ferdinard Ludwig Philipp Cantor

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Born March 3, 1845, Georg Ferdinard Ludwig Philipp Cantor, begin his life in the northwestern corner named Russia within the well-populated merchant colony of Saint Petersburg. The oldest of six children, Cantor was a great violinist. Taking after his grandfather, Franz Bohm (1788-1846) who played in a Russian imperial orchestra. Opposite from his grandfather was Cantor’s father a member among the Saint Petersburg stock exchange, and he was an ace at that, for that the money Cantor’s father would leave Cantor a very large inheritance which will fund his research and education thru out his lifetime. During the year 1856 Cantor just eleven years old will watch his father become ill and uproot the family first traveling Wiesbaden, Germany, but

Pure set theory deals exclusively with sets, so the only sets under consideration are those whose members are also sets. The theory of the hereditarily-finitesets, namely those finite sets whose elements are also finite sets, the elements of which are also finite, and so on, is formally equivalent to arithmetic. So, the essence of set theory is the study of infinite sets, and therefore it can be defined as the mathematical theory of the actual—as opposed to potential—infinite.” (Bagaria)

An example of the philosophy which he worked on look as followed.

Fig. 1. Theorem. |Q|=|N|, where Q={rationals}. Proof. First we prove it for positive ratioals. (1,1) (2,1) (1,2) (3,1) (2,2) (1,3) (4,1) (3,2) ... Write Each pair as a Fraction: 1/1 2/1 1/2 3/1 2/2 1/3 4/1 3/2 ... Delete any repetitions of earlier terms: 1/1 2/1 1/2 3/1 1/3 4/1 3/2 ... Match with positive integers: 1 2 3 4 5 6 7 ... Finally, to get all rational numbers, use the “alternating signs

Two people that spoke out against his teaching were his idols Henri Poincare and Leopold Kronecker. With Kronecker even go as far as to public opposition and personal attacks, saying that Cantor was “renegade” along with becoming a “corrupter of youth.” These thoughts is because Kronecker believes that algebraic numbers are countable, and that were numbers that are transcendental are uncountable. Around this time in 1884, Cantor would face depression for the first time until the end of his life. Even thru his fight with depression, Cantor would attend the first International Congress of Mathematicians in 1897. Here Cantor would relight his friendship with

*…show more content…*Pure set theory deals exclusively with sets, so the only sets under consideration are those whose members are also sets. The theory of the hereditarily-finitesets, namely those finite sets whose elements are also finite sets, the elements of which are also finite, and so on, is formally equivalent to arithmetic. So, the essence of set theory is the study of infinite sets, and therefore it can be defined as the mathematical theory of the actual—as opposed to potential—infinite.” (Bagaria)

An example of the philosophy which he worked on look as followed.

Fig. 1. Theorem. |Q|=|N|, where Q={rationals}. Proof. First we prove it for positive ratioals. (1,1) (2,1) (1,2) (3,1) (2,2) (1,3) (4,1) (3,2) ... Write Each pair as a Fraction: 1/1 2/1 1/2 3/1 2/2 1/3 4/1 3/2 ... Delete any repetitions of earlier terms: 1/1 2/1 1/2 3/1 1/3 4/1 3/2 ... Match with positive integers: 1 2 3 4 5 6 7 ... Finally, to get all rational numbers, use the “alternating signs

*…show more content…*Two people that spoke out against his teaching were his idols Henri Poincare and Leopold Kronecker. With Kronecker even go as far as to public opposition and personal attacks, saying that Cantor was “renegade” along with becoming a “corrupter of youth.” These thoughts is because Kronecker believes that algebraic numbers are countable, and that were numbers that are transcendental are uncountable. Around this time in 1884, Cantor would face depression for the first time until the end of his life. Even thru his fight with depression, Cantor would attend the first International Congress of Mathematicians in 1897. Here Cantor would relight his friendship with