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# A History of Math

History of Math Zeno of Elea Zeno of Elea is a Greek mathematician He would however be better described as a philosopher Little is known about his life for none of his own writings have survived Most of what is known about him comes from the writings of Aristotle Zeno is said to have lived during the fifth century BC in the Greek town of Elea in southern Italy Zeno is important to the study of Math History because of his major contributions the paradoxes and some other minor contributions The most noted of Zenos works are his paradoxes Those dealing with plurality and with motion These were written in response to a theory circulating through the region concerning what we today would call a timespace continuum The other Greek philosophers and mathematicians thought that the world was a plurality of points and instants1 This theory was started by the Pathagoreans They said the world had continuity To contradict them Zeno took their arguments for continuity to an extreme at which point they became absurd To argue against plurality Zeno said that if they are a continuous number of points then there is a given number of them Yet if they are finite they cannot be infinite and plural The whole point of his argument is to bring his opponents argument to a contradiction of logic This was a typical argument against plurality Similar to Zenos argument against plurality is his argument against motion He did not truly believe that motion as given by the senses exists These paradoxes built around the argument of an infinite being finite make up the majority of his world view The first paradox of motion is called the Dichotomy It basically says that for an object to travel a given distance it must first travel half that distance A runner must run 12

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