Infinity Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.Anti-spam check. Do not fill this in! ===Geometry=== Until the end of the 19th century, infinity was rarely discussed in [[geometry]], except in the context of processes that could be continued without any limit. For example, a [[line (geometry)|line]] was what is now called a [[line segment]], with the proviso that one can extend it as far as one wants; but extending it ''infinitely'' was out of the question. Similarly, a line was usually not considered to be composed of infinitely many points, but was a location where a point may be placed. Even if there are infinitely many possible positions, only a finite number of points could be placed on a line. A witness of this is the expression "the [[locus (mathematics)|locus]] of ''a point'' that satisfies some property" (singular), where modern mathematicians would generally say "the set of ''the points'' that have the property" (plural). One of the rare exceptions of a mathematical concept involving [[actual infinity]] was [[projective geometry]], where [[points at infinity]] are added to the [[Euclidean space]] for modeling the [[perspective (graphical)|perspective]] effect that shows [[parallel lines]] intersecting "at infinity". Mathematically, points at infinity have the advantage of allowing one to not consider some special cases. For example, in a [[projective plane]], two distinct [[line (geometry)|lines]] intersect in exactly one point, whereas without points at infinity, there are no intersection points for parallel lines. So, parallel and non-parallel lines must be studied separately in classical geometry, while they need not to be distinguished in projective geometry. Before the use of [[set theory]] for the [[foundation of mathematics]], points and lines were viewed as distinct entities, and a point could be ''located on a line''. With the universal use of set theory in mathematics, the point of view has dramatically changed: a line is now considered as ''the set of its points'', and one says that a point ''belongs to a line'' instead of ''is located on a line'' (however, the latter phrase is still used). In particular, in modern mathematics, lines are ''infinite sets''. Summary: Please note that all contributions to Christianpedia may be edited, altered, or removed by other contributors. If you do not want your writing to be edited mercilessly, then do not submit it here. You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource (see Christianpedia:Copyrights for details). Do not submit copyrighted work without permission! Cancel Editing help (opens in new window) Discuss this page