{"id":3960,"date":"2011-09-05T06:01:00","date_gmt":"2011-09-05T11:01:00","guid":{"rendered":"http:\/\/www.webliminal.com\/webliminalblog\/uncategorized\/links-for-2011-09-05"},"modified":"2011-09-09T09:42:46","modified_gmt":"2011-09-09T14:42:46","slug":"mathematical-induction-again","status":"publish","type":"post","link":"http:\/\/www.webliminal.com\/webliminalblog\/teaching\/mathematical-induction-again","title":{"rendered":"Mathematical Induction &#8211; again"},"content":{"rendered":"<p><a href=\"http:\/\/webliminal.com\/images\/sidepics\/sp59.jpg\"><img loading=\"lazy\" decoding=\"async\" class=\"alignleft\" style=\"margin-left: 22px; margin-right: 22px;\" src=\"http:\/\/webliminal.com\/images\/sidepics\/cwdata\/sp59.jpg\" alt=\"Sassafras leaves, Fredericksburg, Va\" width=\"160\" height=\"120\" align=\"left\" \/><\/a>Teaching the course titled Theoretical Foundations of Computing always presents the problem of (re)introducing studentens to the application and use of the Principle of Mathematical Induction. This link is to one discussion that I think will be helpful to my students.<\/p>\n<ul class=\"delicious\">\n<li>\n<div class=\"delicious-link\"><a href=\"http:\/\/www.math.umaine.edu\/~farlow\/sec16.pdf\">Section 1.6 Proof by Induction<\/a><\/div>\n<div class=\"delicious-extended\">&#8220;The Principle of Mathematical Induction is a method of proof normally\u00c2\u00a0used to prove that a proposition is true for all natural numbers 1,2,3,\u00e2\u20ac\u00a6 \u00c2\u00a0 \u00c2\u00a0 \u00c2\u00a0 \u00c2\u00a0 \u00c2\u00a0 \u00c2\u00a0, although there are many variations of the basic method. \u00c2\u00a0The method is\u00c2\u00a0particularly important in discrete mathematics, and one often sees theorems\u00c2\u00a0proven by induction in areas like computer science. \u00c2\u00a0The technique is so\u00c2\u00a0intuitive and familiar that it sometimes is used without reference to its use. \u00c2\u00a0 \u00c2\u00a0For example, suppose someone tells you they are going to color the natural\u00c2\u00a0numbers 1,2,3, \u00e2\u20ac\u00a6 \u00c2\u00a0 with some color and that the number 1 will be colored\u00c2\u00a0blue, and that if a given number is colored blue, then the next number will also\u00c2\u00a0be colored blue. \u00c2\u00a0 Is there any doubt in your mind that all the numbers will be\u00c2\u00a0colored blue? \u00c2\u00a0Of course not. \u00c2\u00a0This is the induction axiom. \u00c2\u00a0 And the good thing\u00c2\u00a0is you don\u00e2\u20ac\u2122t have to proof it. \u00c2\u00a0It is an axiom&#8221;<\/div>\n<div class=\"delicious-tags\">(tags: <a href=\"http:\/\/www.delicious.com\/ernestackermann\/induction\">induction<\/a> <a href=\"http:\/\/www.delicious.com\/ernestackermann\/recursion\">recursion<\/a>)<\/div>\n<\/li>\n<\/ul>\n<!-- AddThis Advanced Settings generic via filter on the_content --><!-- AddThis Share Buttons generic via filter on the_content -->","protected":false},"excerpt":{"rendered":"<p>Teaching the course titled Theoretical Foundations of Computing always presents the problem of (re)introducing studentens to the application and use of the Principle of Mathematical Induction. This link is to one discussion that I think will be helpful to my students. Section 1.6 Proof by Induction &#8220;The Principle of Mathematical Induction is a method of [&hellip;]<!-- AddThis Advanced Settings generic via filter on get_the_excerpt --><!-- AddThis Share Buttons generic via filter on get_the_excerpt --><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[880,879,538],"class_list":["post-3960","post","type-post","status-publish","format-standard","hentry","category-teaching","tag-cpsc326","tag-induction","tag-theoretical-computing"],"_links":{"self":[{"href":"http:\/\/www.webliminal.com\/webliminalblog\/wp-json\/wp\/v2\/posts\/3960","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.webliminal.com\/webliminalblog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.webliminal.com\/webliminalblog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.webliminal.com\/webliminalblog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/www.webliminal.com\/webliminalblog\/wp-json\/wp\/v2\/comments?post=3960"}],"version-history":[{"count":4,"href":"http:\/\/www.webliminal.com\/webliminalblog\/wp-json\/wp\/v2\/posts\/3960\/revisions"}],"predecessor-version":[{"id":3983,"href":"http:\/\/www.webliminal.com\/webliminalblog\/wp-json\/wp\/v2\/posts\/3960\/revisions\/3983"}],"wp:attachment":[{"href":"http:\/\/www.webliminal.com\/webliminalblog\/wp-json\/wp\/v2\/media?parent=3960"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.webliminal.com\/webliminalblog\/wp-json\/wp\/v2\/categories?post=3960"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.webliminal.com\/webliminalblog\/wp-json\/wp\/v2\/tags?post=3960"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}