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 historical 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 mathematicians of the time looked at ********** science, and he revolutionized the way the world looks at numbers.

***** 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 them in the late 1800s, ***** some ***** 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 did ***** get other mathematicians thinking about problems ***** had plagued them for years, he changed the ***** they ***** at numbers in general - it made ***** question ***** ***** actually are.

How did Cantor's theories affect society? ***** work, which he attributed to God's divine w*****dom showing him the solutions, ***** the way ma*****maticians looked at their work. It also stirred up interest in m*****hematics that had waned dur*****g the Victorian era. Even more importantly, his theories spilled over into many other innovations of the day, including the atomistic statistical *****rmodynamics, stop-motion photography, and even the color-plane type ***** painting by Gauguin ***** Bernard (Everdell 46). ***** addition, Cantor's ********** ***** 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 ***** theories ***** *****s to create, think, prove, and disprove, and so, his work ***** only *****d a ***** underst*****ndable and workable form ***** arithmetic, it created new ***** and ***** art forms ***** changed society and how society looked at science. When people began to understand that mathematics could influence everything from photography to art and *****, they took a greater interest in mathematics and philosophical thought, which ***** turn led to ***** more innovation ***** scientific thinking. In fact, to*****, 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 ***** ***** "***** 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 ***** mathematics, and encouraged people to think *****ly about just what numbers really were.

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

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