{"id":521003,"date":"2026-07-25T06:44:00","date_gmt":"2026-07-25T06:44:00","guid":{"rendered":"https:\/\/livelycity.com\/switzerland\/why-is-x-1-frac1x-mathematics-stack-exchange\/"},"modified":"2026-07-25T06:44:00","modified_gmt":"2026-07-25T06:44:00","slug":"why-is-x-1-frac1x-mathematics-stack-exchange","status":"publish","type":"post","link":"https:\/\/livelycity.com\/switzerland\/why-is-x-1-frac1x-mathematics-stack-exchange\/","title":{"rendered":"Why is $x^{-1} = \\frac{1}{x}$? &#8211; Mathematics Stack Exchange"},"content":{"rendered":"<p>@turkeyhundt I don&#8217;t like appealing to &#8220;common sense&#8221; results like this because it would lead one to believe that negative binomials (for example) aren&#8217;t a thing due to the factorial function, and yet there is another definition that works (generalized version). I am after something a little more rigorous.<\/p>\n<p>\u00a0<a href=\"https:\/\/math.stackexchange.com\/questions\/1881811\/why-is-x-1-frac1x\" target=\"_blank\" class=\"\">https:\/\/math.stackexchange.com\/questions\/1881811\/why-is-x-1-frac1x<\/a>\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"<p>@turkeyhundt I don&#8217;t like appealing to &#8220;common sense&#8221; results like this because it would lead one to believe that negative binomials (for example) aren&#8217;t a&#8230;<\/p>\n","protected":false},"author":0,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[8],"tags":[],"class_list":["post-521003","post","type-post","status-publish","format-standard","hentry","category-zurich","wpcat-8-id"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/posts\/521003","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/types\/post"}],"replies":[{"embeddable":true,"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/comments?post=521003"}],"version-history":[{"count":0,"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/posts\/521003\/revisions"}],"wp:attachment":[{"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/media?parent=521003"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/categories?post=521003"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/livelycity.com\/switzerland\/wp-json\/wp\/v2\/tags?post=521003"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}