Infinity: Difference between revisions

Since the time of the [[Greek mathematics|ancient Greeks]], the [[Infinity (philosophy)|philosophical nature of infinity]] was the subject of many discussions among philosophers. In the 17th century, with the introduction of the [[infinity symbol]]<ref name=":1">{{Cite web|url=https://www.math.tamu.edu/~dallen/masters/infinity/infinity.pdf|title=The History of Infinity|last=Allen|first=Donald|date=2003|website=Texas A&M Mathematics|url-status=live|archive-url=|archive-date=|access-date=2019-11-15}}</ref> and [[infinitesimal calculus]], mathematicians began to work with [[infinite series]] and what some mathematicians (including [[Guillaume de l'Hôpital|l'Hôpital]] and [[Johann Bernoulli|Bernoulli]])<ref name="Jesseph" /> regarded as infinitely small quantities, but infinity continued to be associated with endless processes.<ref>The [[ontological]] status of infinitesimals was unclear, but only some mathematicians regarded infinitesimal as a quantity that is smaller (in magnitude) than any positive number. Others viewed it either as an artefact that makes computation easier or as a small quantity that can be made smaller and smaller until the quantity in which it is involved reaches eventually a [[limit (mathematics)|limit]].{{citation needed|date=November 2019}}</ref> As mathematicians struggled with the foundation of the calculus, it remained unclear whether infinity could be considered as a number or magnitude and, if so, how this could be done.<ref name=":1" /> At the end of the 19th century, [[Georg Cantor]] enlarged the mathematical study of infinity by studying [[infinite set]]s and [[transfinite number|infinite number]]s, showing that they can be of various sizes.<ref name=":1" /><ref>{{cite book