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 mathematics and what that did for society. ***** Cantor's set theory changed the way mathematicians of the time looked at their 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 of an infinite set of real numbers, called transfinite sets, or the "set the*****y." In addition, Cantor found that real numbers were not countable, while algebraic ***** were countable (Breen). Cantor's 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 ***** thought of our time. Not only did Cantor get other mathematicians thinking about problems that had plagued them for years, he changed the way they ***** at numbers in general - it made them ***** ***** numbers actually are.

How did ***** theories affect *****? Cantor's work, which he attributed to God's divine w*****dom showing him the solutions, changed the way mathematicians looked at ***** work. It also stirred up interest in ***** that ***** waned dur*****g the Victorian era. Even more importantly, his *****ories spilled over into many other innovations of the day, including the atomistic statistical *****rmodynamics, stop-motion photography, ***** even the color-plane type ***** painting by Gauguin and Bernard (Everdell 46). ***** add*****ion, Cantor's works ***** inspired philosophical thought in any number of his contemporaries, because ***** like Bertrand Russell and Ludwig Wittgenstein turned to philosophical thought ***** explain and even try to disprove Cantor's *****ories. ***** ***** theories ***** *****s to create, think, prove, and dis*****, and so, his work not only *****d a ***** understandable and ********** form ***** arithmetic, it created new thought and new art forms ***** changed *****ciety and how society looked at science. When people began to understand that mathematics could influence everything from pho*****graphy to ***** and *****, they took a greater interest in mathematics and philosophical thought, which ***** turn led to even more innovation and scientific *****. 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 lasting models ***** s*****ed his ***** were "***** 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.

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

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