{"id":10577,"date":"2015-01-24T11:49:46","date_gmt":"2015-01-24T16:49:46","guid":{"rendered":"http:\/\/mjtsai.com\/blog\/?p=10577"},"modified":"2015-01-31T12:57:38","modified_gmt":"2015-01-31T17:57:38","slug":"creating-the-natural-numbers-from-first-principles","status":"publish","type":"post","link":"https:\/\/mjtsai.com\/blog\/2015\/01\/24\/creating-the-natural-numbers-from-first-principles\/","title":{"rendered":"Creating the Natural Numbers From First Principles"},"content":{"rendered":"<p><a href=\"http:\/\/www.fewbutripe.com\/swift\/math\/2015\/01\/20\/natural-numbers.html\">Brandon Williams<\/a>:<\/p>\n<blockquote cite=\"http:\/\/www.fewbutripe.com\/swift\/math\/2015\/01\/20\/natural-numbers.html\">\n<p>Turns out, natural numbers can be constructed from two <a href=\"http:\/\/en.wikipedia.org\/wiki\/Peano_axioms\">basic objects<\/a>. First, we start with the &ldquo;smallest&rdquo; member of the naturals, called <code>Zero<\/code>. Then we have a function <code>Succ<\/code> (the successor function) that takes a natural and returns the next natural.<\/p>\n<\/blockquote>\n<p>Update (2015-01-31): The <a href=\"http:\/\/www.fewbutripe.com\/swift\/math\/2015\/01\/27\/solutions-to-natural-numbers.html\">solutions<\/a> to the exercises.<\/p>","protected":false},"excerpt":{"rendered":"<p>Brandon Williams: Turns out, natural numbers can be constructed from two basic objects. First, we start with the &ldquo;smallest&rdquo; member of the naturals, called Zero. Then we have a function Succ (the successor function) that takes a natural and returns the next natural. Update (2015-01-31): The solutions to the exercises.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"apple_news_api_created_at":"","apple_news_api_id":"","apple_news_api_modified_at":"","apple_news_api_revision":"","apple_news_api_share_url":"","apple_news_coverimage":0,"apple_news_coverimage_caption":"","apple_news_is_hidden":false,"apple_news_is_paid":false,"apple_news_is_preview":false,"apple_news_is_sponsored":false,"apple_news_maturity_rating":"","apple_news_metadata":"\"\"","apple_news_pullquote":"","apple_news_pullquote_position":"","apple_news_slug":"","apple_news_sections":"\"\"","apple_news_suppress_video_url":false,"apple_news_use_image_component":false,"footnotes":""},"categories":[4],"tags":[263,259,71,901],"class_list":["post-10577","post","type-post","status-publish","format-standard","hentry","category-programming-category","tag-theory","tag-math","tag-programming","tag-swift-programming-language"],"apple_news_notices":[],"_links":{"self":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts\/10577","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/comments?post=10577"}],"version-history":[{"count":2,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts\/10577\/revisions"}],"predecessor-version":[{"id":10618,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/posts\/10577\/revisions\/10618"}],"wp:attachment":[{"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/media?parent=10577"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/categories?post=10577"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mjtsai.com\/blog\/wp-json\/wp\/v2\/tags?post=10577"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}