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


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Mathematics

***** Cantor

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

***** Cantor was a brilliant mathematician ***** philosopher who developed the modern ma*****matical idea of infin*****y, along with the idea of an infinite set ***** real numbers, called transfinite sets, or ***** "set the*****y." In addition, Cantor found that real numbers were not countable, while algebraic numbers were countable (Breen). ********** views were quite controversial when he first developed them in the late 1800s, and 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 ***** they looked at ***** in general - it made them question ***** numbers actually are.

***** did *****'s theories affect *****? Cantor's work, which he attributed to God's divine w*****dom showing him the solutions, ***** the way ma*****aticians looked at their work. It also stirred up interest in ***** that had waned dur*****g 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 ***** painting by Gauguin and Bernard (Everdell 46). ***** add*****ion, ***** works ***** inspired philosophical thought in any number of ***** contemporaries, because ma*****maticians like Bertrand Russell and Ludwig Wittgenstein turned to philosophical ***** ***** explain and even try to disprove Cantor's theories. ***** set theories inspired others to create, think, prove, and disprove, and so, his work ***** ***** *****d a more underst*****ndable and ********** form ***** arithmetic, it created new thought and new art forms that changed *****ciety and how society looked at science. When people began to understand that mathematics could influence everything from pho*****graphy to ***** and science, they took a greater interest in mathematics and philosophical thought, ***** in turn led to even more ********** and scientific thinking. In fact, today, m***** scientists and mathematicians feel Cantor's work represented a real paradigm shift, or a r*****dical change in mathematical and philosophical ***** ("Cantor"). Two of his l*****ting models that showed his theories ***** "*****'s Comb," which showed all points were disconnected from each other, and "Cantor's Dust," which calls these ***** sets "fractal dust" (Breen). Cantor's work *****ly revolutionized mathematics, ***** encouraged people to think *****ly about just what numbers really were.

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

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