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
France before being exiled. Napoleon then lived in Longwood House. Dying of cancer on May
On November 10, 1848, his parents migrated to America. When they arrived they settled in New York where they married. His Parents were loving, caring and wise.(www.marxists.org)
mind was focused on other things other than his father. He thought that if he
Hemingway writes his works so that not everything is as it seems. It makes readers take a deeper insight about what he’s writing about. In the story ‘Hills Like White Elephants’ he writes about an operation. Now from the surface, it seems as if they are just going on a trip and when he brings up this operation, readers don’t understand that they are talking about an abortion. The story has to be read a few times, before readers really understand that the argument is about a pregnancy and how the man wants the abortion. This is how Hemingway wanted to write his story. By using his dialogue and symbolism, Hemingway plays everything out in a way that makes readers analyze the story.
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
of his father and his father before him. He came to a certain point in his life where one
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.
then, As a result, He gave up on his father and began to live his life completely separated from
Ernest Hemingway is an incredible writer, known for what he leaves out of stories not for what he tells. His main emphasis in Hills Like White Elephants seems to be symbolism. Symbolism is the art or practice of using symbols, especially by investing things with a symbolic meaning or by expressing the invisible or intangible by means of visible or sensuous representations (merriam-webster.com). He uses this technique to emphasize the importance of ideas, once again suggesting that he leaves out the important details of the story by symbolizing their meaning.
began to worry his parents, and by the advice of his grandfather he was sent to
raising them on his own was too much for him and soon began looking for a
...as pulled into this situation by chance, and it was left in his hands to justify his father's death. He did what he had to do according to his own manner.
In the short story by Ernest Hemingway, "Hills Like White Elephants," a couple is delayed at a train station en route to Madrid and is observed in conflict over the girl's impending abortion. In his writing, Hemingway does not offer any commentary through a specific character's point of view, nor, in the storytelling, does he offer his explicit opinions on how to feel or think about the issues that emerge. The narrative seems to be purely objective, somewhat like a newspaper or journal article, and in true Hemingway form the story ends abruptly, without the couple's conflict clearly being resolved. The ambiguity of the ending has been a subject of much debate; however, the impact of what is not said in words can be gleaned through the symbolism of their surroundings. Upon examination of the setting, the couple's final choice becomes instantly apparent.
To understand the nature-society relationship means that humans must also understand the benefits as well as problems that arise within the formation of this relationship. Nature as an essence and natural limits are just two of the ways in which this relationship can be broken down in order to further get an understanding of the ways nature and society both shape one another. These concepts provide useful approaches in defining what nature is and how individuals perceive and treat