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


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Mathematics

George Cantor

***** purpose of the paper is to develop a concept ***** the connection between mathematics and society from a his*****ric*****l perspective. Specifically, it will discuss the subject, what George Cantor accomplished for ***** and what that did for *****. George 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 mathematician ***** philosopher who developed the modern mathematical idea of infin*****y, along with the idea of an infinite set of real numbers, called transfinite sets, or ***** "set *****." In addition, Cant***** found that real numbers were not countable, while algebraic ***** 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 ("Transf*****ite Number"), however, his work is recognized as some of the most important mathematical thought of our time. Not only ***** Cantor get other mathematicians thinking about problems that had plagued them for years, he changed the ***** they ***** at numbers in general - it made ***** question what ***** actually are.

How did Cantor's theories affect society? ***** work, which he attributed to God's divine w*****dom showing him the solutions, changed the way ma*****maticians looked at their work. It also stirred up interest in m*****hematics that ***** waned during the Victorian era. Even more importantly, his theories spilled over into many ***** innovations of the day, including the atomistic statistical *****rmodynamics, stop-motion photography, ***** even the color-plane type of painting by Gauguin and Bernard (Everdell 46). In add*****ion, Cantor's works ***** inspired philosophical thought in any number of his contemporaries, because ma*****maticians like Bertrand Russell and Ludwig Wittgenstein turned to philosophical ***** to explain and even try to disprove Cantor's theories. ***** ***** theories inspired others to create, think, prove, and disprove, and so, his work ***** ***** created a more understandable and workable form ***** arithmetic, it created new thought and ***** art forms that changed *****ciety ***** how society looked at science. When people began to understand ***** mathematics could influence everything from pho*****graphy to art and *****, they took a greater interest in mathematics and philosophical thought, which in turn led to ***** more ********** ***** scientific *****. In fact, to*****, many scientists and mathematicians feel Cantor's work represented a real paradigm shift, or a r*****dical change in ***** and philosophical thought ("Cantor"). Two of his l*****ting models that s*****ed his ***** ***** "Cantor'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 really revolutionized mathematics, ***** encouraged people to think *****ly about just ***** numbers really were.

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

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