Editing Chrysippus (section)

== Mathematics ==
[[File:Kegelstumpf.png|thumb|right|The puzzle of Democritus. If a cone is sliced horizontally, are the surfaces produced equal or unequal?]]

Chrysippus regarded [[Physical body|bodies]], surfaces, [[Line (geometry)|lines]], [[Location (geography)|places]], the [[Vacuum|void]] and [[time]] as all being [[Infinite divisibility|infinitely divisible]].<ref name="gould116">{{Harvnb|Gould|1970|p=116}}</ref> He determined one of the principal features of the [[infinite set]]: since a man and a finger have an [[Infinity|infinite]] number of parts as do the universe and a man, it cannot be said that a man has more parts than his finger, nor that the universe has more parts than a man.<ref name="gould117">{{Harvnb|Gould|1970|p=117}}</ref>

Chrysippus also responded to a problem first posed by [[Democritus]].<ref>Plutarch, ''De Communibus Notitiis'', 1079F</ref> If a [[Cone (geometry)|cone]] is divided by a [[Plane (geometry)|plane]] parallel to its base, are the surfaces of the segments equal or unequal? If they are equal, then the cone becomes a [[Cylinder (geometry)|cylinder]]; if they are unequal, then the surface of the cone must be [[Step function|stepped]].<ref name="gould117"/> The reply of Chrysippus was that the surfaces are both equal and unequal.<ref name="gould118">{{Harvnb|Gould|1970|p=118}}</ref> Chrysippus was, in effect, negating the [[law of excluded middle]] with respect to the equal and unequal, and thus he may have anticipated an important principle of modern [[infinitesimal calculus]], namely, the [[Limit (mathematics)|limit]] and the process of [[Convergent series|convergence towards a limit]].<ref name="gould118"/>

Chrysippus was notable for claiming that "[[1 (number)|one]]" is a [[number]]. One was not always considered a number by the ancient Greeks since they viewed one as that by which things are measured. [[Aristotle]] in his ''[[Metaphysics (Aristotle)|Metaphysics]]'' wrote, "... a measure is not the things measured, but the measure or the One is the beginning of number."<ref name="heath69">{{Harvnb|Heath|1921|p=69}}</ref> Chrysippus asserted that one had "magnitude one" ({{langx|el|πλῆθος ἕν}}),<ref>[[Iamblichus]], ''in Nicom''., ii. 8f; [[Syrianus]], ''in Arist. Metaph.'', Kroll 140. 9f.</ref> although this was not generally accepted by the Greeks, and [[Iamblichus]] wrote that "magnitude one" was a contradiction in terms.<ref name="heath69"/>