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 even numbers, squares, cubes, and roots to equations; that the number of points in a line segment is equal to the number of points in an infinite line, a plane and all mathematical space; and that the number of transcendental numbers, values such as pi(3.14159) and e(2.71828) that can never be the solution to any algebraic equation, were much larger than the number of integers. Before in mathematics, infinity had been a sacred subject. Previously, Gauss had stated that infinity should only be used as a way of speaking and not as a mathematical
In a well-written short story, different literary elements and terms are incorporated into the story by the author. Ernest Hemingway frequently uses various literary elements in his writing to entice the reader and enhance each piece that he writes. In Hills Like White Elephants, Hemingway uses symbols to teach the reader certain things that one may encounter during daily life. Symbolism may be defined as relating to, using, or proceeding by means of symbols (Princeton). The use of symbols in Hills Like White Elephants is utterly important to the plot line and to the fundamental meaning of the story. Through this use of symbolism, the reader can begin to reveal the hidden themes in this short story.
He continually shows his inability to accept blame and fully believes his problems are a result of another person’s actions, with the first person possibly being the one who gave him his name. He was very rebellious and would not listen or cooperate with anyone. An example of this was his mother's concern over what was becoming of him and her decision to take him to church. “When he saw the big lighted church, he jerked out of his grasp and ran”. It was clear his mother had lost all control of him at this time.
Above all, Hemingway wants to make the reader understand how one person’s selfishness and needs can manage to manipulate another one by pretending to care. He also proves how women at times can be easily influenced by the people they love. They are tricked into believing they are everything to them. He shows a couple’s different point of views and their inability to understand and listen one another. For the most part, Hemingway send the message that everything is possible. A woman does not need a man’s approval for anything. Women are successful, strong and can overcome the biggest things in life.
He began writing about his hypothesis/ idea in 1864-65, and published the results in 1866. It was not until 1900 that his published findings were
Meter, M. An Analysis of the Writing Style of Ernest Hemingway. Texas: Texas College of Arts and Industries, 2003.
of his father and his father before him. He came to a certain point in his life where one
began to worry his parents, and by the advice of his grandfather he was sent to
France before being exiled. Napoleon then lived in Longwood House. Dying of cancer on May
raising them on his own was too much for him and soon began looking for a
France. He was a descendent of a very old French family. As a boy, Maupassant
“Hills like White Elephants” by Ernest Hemingway is about a couple, the American and Jig, who contemplate whether or not to have an abortion. The premise of the story seems simple enough, but the outcome is highly debated. Critics argue that the baby was kept by the couple ( Renner ) and others claim the baby was aborted.( Fletcher ) Others have even simplified the story, claiming that the issue was not resolved because the couple was drunk by the end of the story. ( Sipiora ) Although the conclusion is in questions many have agreed with the idea that the couples relationship would be changed and would end prematurely. ( Wyche ) Dialogue is the main technique in conveying this argument but we can only understand the complexity of Hemingway’s work by looking at the story as a whole. By looking at the many symbols, intrinsically and
then, As a result, He gave up on his father and began to live his life completely separated from
Renner, Stanley "Moving to the Girl's Side of `Hills Like White Elephants'." The Hemingway Review, 15 (1) (Fall 1995): 27-41. As Rpt. in Wyche, David "Letting the Air into a Relationship: Metaphorical Abortion in `Hills Like White Elephants'. The Hemingway Review, 22 (1) (Fall 2002): 56-71. EBSCOhost.