{"id":600,"date":"2012-11-02T05:00:09","date_gmt":"2012-11-02T12:00:09","guid":{"rendered":"http:\/\/zackmdavis.net\/blog\/?p=600"},"modified":"2012-11-01T22:22:32","modified_gmt":"2012-11-02T05:22:32","slug":"subscripting-as-function-composition","status":"publish","type":"post","link":"http:\/\/zackmdavis.net\/blog\/2012\/11\/subscripting-as-function-composition\/","title":{"rendered":"Subscripting as Function Composition"},"content":{"rendered":"<p>Dear reader, don't laugh: I had thought I already understood subsequences, but then it turned out that I was mistaken. I should have noticed the vague, unverbalized discomfort I felt about the subscripted-subscript notation, (<em>a<sub>n<sub>k<\/sub><\/sub><\/em>). But really it shouldn't be confusing at all: as Bernd S. W. Schr\u00f6der points out in his <em>Mathematical Analysis: A Concise Introduction<\/em>, it's just a function composition. If it helps (it helped me), say that (<em>a<sub>n<\/sub><\/em>) is mere <em>syntactic sugar<\/em> for <em>a<\/em>(<em>n<\/em>): \u2115 \u2192 \u211d, a function from the naturals to the reals. And (<em>a<sub>n<sub>k<\/sub><\/sub><\/em>) is just the composition <em>a<\/em>(<em>n<\/em>(<em>k<\/em>)), with <em>n<\/em>(<em>k<\/em>): \u2115 \u2192 \u2115 being a strictly increasing function from the naturals to the naturals.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Dear reader, don't laugh: I had thought I already understood subsequences, but then it turned out that I was mistaken. I should have noticed the vague, unverbalized discomfort I felt about the subscripted-subscript notation, (ank). But really it shouldn't be &hellip; <a href=\"http:\/\/zackmdavis.net\/blog\/2012\/11\/subscripting-as-function-composition\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[7],"tags":[33,45],"_links":{"self":[{"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/posts\/600"}],"collection":[{"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/comments?post=600"}],"version-history":[{"count":7,"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/posts\/600\/revisions"}],"predecessor-version":[{"id":614,"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/posts\/600\/revisions\/614"}],"wp:attachment":[{"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/media?parent=600"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/categories?post=600"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/zackmdavis.net\/blog\/wp-json\/wp\/v2\/tags?post=600"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}