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

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***** Cantor

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

***** Cantor was a brilliant mathematician ***** philosopher who developed the modern mathematical idea of infinity, along with the idea ***** an infinite set of real numbers, called transfinite sets, or ***** "set *****." 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, and some mathematicians today question some ***** his hypothesis ("Transfinite Number"), however, his work is recognized as some of the most important mathematical thought ***** our time. Not only did ***** get other mathematicians thinking about problems ***** had plagued them for years, he changed the ***** they looked at numbers in general - it made ***** ***** what numbers actually are.

***** did Cantor's theories affect society? Cantor's work, which he attributed to God's divine wisdom showing him the solutions, ***** the way ma*****maticians ***** at their work. It also stirred up interest in mathematics that ***** waned dur*****g the Victorian era. Even more importantly, ***** *****ories spilled over into many other innovations of the day, including the atomistic statistical thermodynamics, stop-motion photography, and even the color-plane type ***** painting by Gauguin ***** Bernard (Everdell 46). In addition, ***** works ***** inspired philosophical thought in any number of his contemporaries, because ma*****maticians like Bertrand Russell and Ludwig Wittgenstein turned to philosophical ***** ***** explain and even try to disprove Cantor's theories. ***** set theories ***** *****s to create, think, prove, and dis*****, and so, his work ***** only *****d a ***** understandable and ********** form ***** arithmetic, it created new thought and ***** art forms that changed *****ciety ***** how society looked at science. When people began to understand that mathematics could influence everything from pho*****graphy to art and *****, they took a greater interest in mathematics and philosophical thought, which ***** turn led to ***** more innovation ***** scientific *****. In fact, today, m***** scientists and mathematicians feel Cantor's work represented a real paradigm shift, or a radical change in mathematical and philosophical ***** ("Cantor"). Two of his l*****ting models that showed his ***** ***** "Cantor's Comb," which showed all points were ********** from each other, and "Cantor's Dust," which calls these disconnected sets "fractal dust" (Breen). Cantor's work really revolutionized mathematics, ***** encouraged ***** to think *****ly about just what numbers really were.

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


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