Georg Cantor Essay

2125 Words Sep 27th, 1999 9 Pages
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
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In 1885 Cantor continued to extend his theory of cardinal numbers and of order types. He extended his theory of order types so that now his previously defined ordinal numbers became a special case. In 1895 and 1897 Cantor published his final double treatise on sets theory. Cantor proves that if A and B are sets with A equivalent to a subset of B and B equivalent to a subset of A then A and
B are equivalent. This theorem was also proved by Felix Bernstein and by Schrö der. The rest of his life was spent in and out of mental institutions and his work nearly ceased completely. Much too late for him to really enjoy it, his theory finally began to gain recognition by the turn of the century. In 1904, he was awarded a medal by the Royal Society of London and was made a member of both the London Mathematical Society and the Society of Sciences in Gottingen. He died in a mental institution on January 6, 1918. Today, Cantor's work is widely used in the many fields of mathematics. His theory on infinite sets reset the foundation of nearly every mathematical field and brought mathematics to its modern form.

II. Infinity

Most everyone is familiar with the infinity symbol . How many is infinitely many? How far away is "from here to infinity"? How big is infinity?
We can't count to infinity. Yet we are

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