{"id":2160,"date":"2013-12-12T15:39:43","date_gmt":"2013-12-12T14:39:43","guid":{"rendered":"http:\/\/www.illc.uva.nl\/lgc\/seminar\/?p=2160"},"modified":"2015-10-06T14:59:19","modified_gmt":"2015-10-06T12:59:19","slug":"logiciclira-session-fenrong-liu-and-imme-van-den-berg","status":"publish","type":"post","link":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/2013\/12\/logiciclira-session-fenrong-liu-and-imme-van-den-berg\/","title":{"rendered":"LIRa Session: Imme van den Berg"},"content":{"rendered":"<p>On Thursday,\u00a0January 9,<strong> <\/strong>we will have a LIRa session with<strong> Imme van den Berg<\/strong>.  Everyone is cordially invited!<\/p>\n<p>Speaker:\u00a0<strong><strong>Imme van den Berg<span style=\"line-height: 6px;\">, <\/span><\/strong><\/strong><span style=\"line-height: 6px;\">(Department of Mathematics, University of Evora)<\/span><br \/>\nTitle:\u00a0<strong>A model for orders of magnitude within Nonstandard Analysis<br \/>\n<\/strong>Date and Time: Thursday, January 9 2014,\u00a0<strong>15:30-17:30<br \/>\n<\/strong>Venue: Science Park 107, Room\u00a0<strong>F1.15<\/strong><\/p>\n<p>Abstract:<br \/>\nMany arguments deal informally with orders of magnitude of numbers. The aim\u00a0of this talk is two-fold, to establish an acceptable axiomatics for orders\u00a0of magnitude and indicate structures which satisfy the axioms or parts of\u00a0them. Our formalization tries to maintain the intrinsic vagueness: orders of\u00a0magnitude should be bounded, but stable under at least some additions.<\/p>\n<p>Due to the Archimedean property and Dedekind completion, such a\u00a0formalization cannot be done with ordinary real numbers, still there is the\u00a0functional approach through <em>O&#8217;s <\/em>and <em>o&#8217;s<\/em>, and more\u00a0generally Van der Corput&#8217;s neutrices, both have some operational\u00a0shortcomings.<\/p>\n<p>Nonstandard Analysis disposes of a natural example of order of magnitude:\u00a0the (external) set of infinitesimals is bounded and closed under addition.\u00a0Adopting the terminology of Van der Corput, we call a <em>neutrix<\/em> a\u00a0additive convex subgroup of the nonstandard reals. An\u00a0<em>external number <\/em>is the set-theoretic sum of a nonstandard real and a neutrix.<\/p>\n<p>The external numbers capture the imprecise boundaries of informal orders of\u00a0magnitude and permit algebraic operations which go beyond the calculus of\u00a0the <em>O&#8217;s <\/em>and\u00a0<em>o&#8217;s<\/em>, allowing for total order with a\u00a0generalized form of Dedekind completion.<\/p>\n<p>In addition we discuss some applications and foundational problems.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>On Thursday,\u00a0January 9, we will have a LIRa session with Imme van den Berg.  Everyone is cordially invited!<br \/>\nSpeaker:\u00a0Imme van den Berg, (Department of Mathematics, University of Evora)<br \/>\nTitle:\u00a0A model for orders of magnitude within Nonstandard Analysis<br \/>\nDate and Time: Thursday, January 9 2014,\u00a015:30-17:30<br \/>\nVenue: Science Park 107, Room\u00a0F1.15<br \/>\nAbstract:<br \/>\nMany arguments deal informally with orders of magnitude of numbers. [&#8230;]<\/p>\n","protected":false},"author":11,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-2160","post","type-post","status-publish","format-standard","hentry","category-events"],"_links":{"self":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts\/2160","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/users\/11"}],"replies":[{"embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/comments?post=2160"}],"version-history":[{"count":20,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts\/2160\/revisions"}],"predecessor-version":[{"id":2162,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/posts\/2160\/revisions\/2162"}],"wp:attachment":[{"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/media?parent=2160"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/categories?post=2160"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.illc.uva.nl\/lgc\/seminar\/wp-json\/wp\/v2\/tags?post=2160"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}