Changes

== History ==

== History ==

The [[Ancient Greece|Ancient Greek]] [[philosopher]] [[Zeno of Elea]] first came up with the idea of this series. The [[paradox]] called "[https://en.m.wikipedia.org/wiki/Zeno's_paradoxes zeno's parodox'] is the result. He believed that it would be impossible to add an [[infinity|infinite]] number of values and get a single [[finite]] value as a result.

The [[Ancient Greece|Ancient Greek]] [[philosopher]] [[Zeno of Elea]] first came up with the idea of this series. The [[paradox]] called "[https://en.m.wikipedia.org/wiki/Zeno's_paradoxes Zeno's paradox]" is the result. He believed that it would be impossible to add an [[infinity|infinite]] number of values and get a single [[finite]] value as a result.

Another Greek philosopher, [[Aristotle]], came up with an answer to the philosophical question. It was [[Archimedes]], however, who came up with a mathematical solution using his [[method of exhaustion]]. He was able to prove that when something is split up into an infinite number of tiny pieces, they will still add up to a single whole when all of them are added back together.<ref>{{cite book|last=Kline|first=M|year=1990|title=Mathematical Thought from Ancient to Modern Times|url=https://archive.org/details/mathematicalthou00klin|publisher=Oxford University Press|pages=[https://archive.org/details/mathematicalthou00klin/page/n438 35]-37}}</ref> The ancient [[China|Chinese]] [[mathematician]] [[Liu Hui]] proved the same thing several hundred years later.<ref>{{cite book|last1=Boyer|first1=C|last2=Merzbach|first2=U|year=1991|title=A History of Mathematics|url=https://archive.org/details/historymathemati00boye_328|publisher=John Wiley and Sons|pages=[https://archive.org/details/historymathemati00boye_328/page/n221 202]-203}}</ref>

Another Greek philosopher, [[Aristotle]], came up with an answer to the philosophical question. It was [[Archimedes]], however, who came up with a mathematical solution using his [[method of exhaustion]]. He was able to prove that when something is split up into an infinite number of tiny pieces, they will still add up to a single whole when all of them are added back together.<ref>{{cite book|last=Kline|first=M|year=1990|title=Mathematical Thought from Ancient to Modern Times|url=https://archive.org/details/mathematicalthou00klin|publisher=Oxford University Press|pages=[https://archive.org/details/mathematicalthou00klin/page/n438 35]-37}}</ref> The ancient [[China|Chinese]] [[mathematician]] [[Liu Hui]] proved the same thing several hundred years later.<ref>{{cite book|last1=Boyer|first1=C|last2=Merzbach|first2=U|year=1991|title=A History of Mathematics|url=https://archive.org/details/historymathemati00boye_328|publisher=John Wiley and Sons|pages=[https://archive.org/details/historymathemati00boye_328/page/n221 202]-203}}</ref>