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Georg Cantor - Essay

Georg Cantor


I.
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 ...

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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 ...

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he did all he could to
suppress Cantor's ideas and ruin his life. Among other things, he delayed or
suppressed completely Cantor's and his followers' publications, belittled his
ideas in front of his students and blocked Cantor's life ambition of gaining a
position at the prestigious University of Berlin. Not all mathematicians were
hostile to Cantor's ideas. Some greats such as Karl Weierstrass, and long-time
friend Richard Dedekind supported his ideas and attacked Kronecker's actions.
However, it was not enough. Cantor simply could not handle it. Stuck in a third-
rate institution, stripped of well-deserved recognition for his work and under
constant attack by Kronecker, he suffered ...

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"Georg Cantor." Essayworld.com. November 27, 2004. Accessed December 22, 2024. http://www.essayworld.com/essays/Georg-Cantor/18117.
"Georg Cantor." Essayworld.com. November 27, 2004. Accessed December 22, 2024. http://www.essayworld.com/essays/Georg-Cantor/18117.
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PAPER DETAILS
Added: 11/27/2004 10:44:34 AM
Category: Biographies
Type: Free Paper
Words: 2069
Pages: 8

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