Essay - Mathematics George Cantor the Purpose of the Paper is to...

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***** Cantor

The purpose of the paper is to develop a concept ***** the connection between mathematics and society from a historic*****l perspective. Specifically, it will discuss the subject, what George Cantor accomplished for ***** and what that did for *****. ***** Cantor's set theory changed the way ma*****maticians of the time looked at their science, and he revolutionized the way the world looks at numbers.

George Cantor was a brilliant m*****hematician and philosopher who developed the modern ma*****matical idea of infin*****y, along with the idea ***** an infinite set of real numbers, called transfinite sets, or ***** "set the*****y." In addition, Cantor found that real ***** were not countable, while algebraic numbers were countable (Breen). ***** views were quite controversial when he first developed t*****m in the late 1800s, ***** some mathematicians today question some of his hypothesis ("Transfinite Number"), however, his work is recognized as some ***** the most important mathematical thought of our time. Not only ***** Cantor get other ***** thinking about problems ***** had plagued them for years, he changed the way they looked at ***** in general - it made them ***** ***** numbers actually are.

How did ********** theories affect society? Cantor's work, which he attributed to God's divine wisdom showing him the solutions, ***** the way ma*****aticians looked at ***** work. It also stirred up interest in ma*****matics that had waned during the Victorian era. Even more importantly, his theories spilled over into many ***** innovations of the day, including the atomistic statistical thermodynamics, stop-motion photography, and even the color-plane type of painting by Gauguin ***** Bernard (Everdell 46). In add*****ion, Cantor's ********** also inspired philosophical thought in any number of ***** contemporaries, because ma*****maticians like Bertrand Russell and Ludwig Wittgenstein turned to philosophical thought ***** explain ***** even try to disprove Can*****r's theories. Cantor's set theories inspired others to create, think, prove, and dis*****, and so, his work not only created a more understandable and ********** form of arithmetic, it created new ***** and ***** art forms ***** changed *****ciety and how society looked at science. When people began to understand that mathematics could influence everything from pho*****graphy to art and science, they took a greater interest in mathematics and philosophical thought, which ***** turn led to ***** more innovation and scientific *****. In fact, today, many scientists and mathematicians feel Cantor's work represented a real paradigm shift, or a radical change in ***** and philosophical thought ("Cantor"). Two ***** his lasting models that showed his theories ***** "***** Comb," which showed all points were disconnected from each other, and "*****'s Dust," which calls these ***** sets "fractal dust" (Breen). Cantor's work really revolutionized mathematics, ***** encouraged ***** to think philosophically about just what numbers really were.

*****, Cantor's mental health deteriorated as he aged, and ***** had several nervous breakdowns in reaction to criticism of ***** *****. Today, many believe he suffered from bipolar disorder ("Cantor"). It is sad to ***** ***** Cantor may have contributed even more to


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