{"id":20461,"date":"2026-09-23T23:01:13","date_gmt":"2026-09-23T13:01:13","guid":{"rendered":"https:\/\/geoffreychen.com\/why-zero-factorial-equals-one\/"},"modified":"2026-09-23T23:01:13","modified_gmt":"2026-09-23T13:01:13","slug":"why-zero-factorial-equals-one","status":"publish","type":"post","link":"https:\/\/geoffreychen.com\/zh\/why-zero-factorial-equals-one\/","title":{"rendered":"0! \u4e3a\u4ec0\u4e48\u7b49\u4e8e 1\uff0c\u800c\u4e0d\u662f 0\uff1f"},"content":{"rendered":"<\/p>\n<p><img data-recalc-dims=\"1\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/public-assets.geoffreychen.com\/wordpress\/articles\/why-zero-factorial-equals-one\/f0a6ced4f9645df3dd7db967.jpg?w=1140&#038;ssl=1\" alt=\"0! \u4e3a\u4ec0\u4e48\u7b49\u4e8e 1\uff0c\u800c\u4e0d\u662f 0\uff1f\" loading=\"lazy\"><\/p>\n<p>\u9636\u4e58\u53ef\u4ee5\u7406\u89e3\u4e3a\u6392\u5217\u6570\u91cf\uff1a3 \u4ef6\u4e0d\u540c\u7269\u54c1\u6709 3\u00d72\u00d71=6 \u79cd\u6392\u6cd5\u3002\u82e5\u4e00\u4ef6\u7269\u54c1\u4e5f\u6ca1\u6709\uff0c\u4f3c\u4e4e\u201c\u6ca1\u6709\u6392\u6cd5\u201d\uff0c\u4f46\u8fd9\u91cc\u6df7\u6dc6\u4e86\u6ca1\u6709\u7269\u54c1\u4e0e\u6ca1\u6709\u7ed3\u679c\u3002\u7a7a\u96c6\u5408\u4ecd\u6709\u4e00\u79cd\u6392\u5217\u2014\u2014\u4ec0\u4e48\u4e5f\u4e0d\u653e\u3001\u4ec0\u4e48\u4e5f\u4e0d\u505a\u7684\u7a7a\u6392\u5217\uff1b\u4e0d\u5b58\u5728\u7b2c\u4e8c\u79cd\u4e0d\u540c\u987a\u5e8f\u3002\u56e0\u6b64 0!=1\u3002<\/p>\n<p>\u540c\u4e00\u7ed3\u8bba\u4e5f\u6765\u81ea\u9636\u4e58\u7684\u9012\u63a8\u89c4\u5219\u3002\u5bf9\u6b63\u6574\u6570 n\uff0cn!=n\u00d7(n\u22121)!\u3002\u628a n \u53d6\u4e3a 1\uff0c\u4fbf\u6709 1!=1\u00d70!\uff1b\u56e0\u4e3a 1!=1\uff0c0! \u53ea\u80fd\u7b49\u4e8e 1\uff0c\u5426\u5219\u8fd9\u6761\u89c4\u5219\u4f1a\u5728\u8fb9\u754c\u7a81\u7136\u65ad\u88c2\u3002\u8fd9\u91cc\u8fd8\u7528\u5230\u201c\u7a7a\u4e58\u79ef\u201d\uff1a\u6ca1\u6709\u4efb\u4f55\u56e0\u5b50\u76f8\u4e58\u65f6\u53d6 1\uff0c\u56e0\u4e3a 1 \u662f\u4e58\u6cd5\u7684\u5355\u4f4d\u5143\uff0c\u4e0d\u4f1a\u6539\u53d8\u968f\u540e\u4e58\u5165\u7684\u6570\u3002<\/p>\n<p>\u6240\u4ee5 0!=1 \u4e0d\u662f\u628a\u201c\u96f6\u4e2a\u4e1c\u897f\u201d\u8bf4\u6210\u201c\u4e00\u4ef6\u4e1c\u897f\u201d\uff0c\u4e5f\u4e0d\u662f\u56e0\u4e3a\u4efb\u4f55\u6570\u4e58\u4ee5\u96f6\u3002\u5b83\u6570\u7684\u662f\u53ef\u884c\u6392\u5217\uff0c\u800c\u4e0d\u662f\u7269\u54c1\u6570\u91cf\uff1b\u7a7a\u6392\u5217\u6070\u597d\u662f\u4e00\u4e2a\u7ed3\u679c\u3002\u8fd9\u4e2a\u8fb9\u754c\u503c\u8ba9\u7ec4\u5408\u516c\u5f0f\u4fdd\u6301\u4e00\u81f4\u3002\u4f8b\u5982\u4ece\u4e94\u4e2a\u4eba\u4e2d\u9009\u96f6\u4e2a\u4eba\uff0c\u9009\u62e9\u65b9\u5f0f\u786e\u5b9e\u53ea\u6709\u4e00\u79cd\uff1a\u8c01\u4e5f\u4e0d\u9009\u3002<\/p>\n<p><a href=\"https:\/\/dlmf.nist.gov\/5.2\" rel=\"nofollow\">https:\/\/dlmf.nist.gov\/5.2<\/a><\/p>\n<p>","protected":false},"excerpt":{"rendered":"","protected":false},"author":17897162,"featured_media":0,"comment_status":"","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_geoff_meta_description_en":"Zero factorial equals one because an empty set has one empty arrangement, while the empty product must preserve the identity and recurrence of multiplication.","_geoff_meta_description_zh":"\u4ece\u6392\u5217\u6570\u91cf\u3001\u9636\u4e58\u9012\u63a8\u5f0f\u548c\u7a7a\u4e58\u79ef\u4e09\u65b9\u9762\u770b\uff0c0! \u7b49\u4e8e 1 \u5e76\u975e\u968f\u610f\u89c4\u5b9a\uff1a\u7a7a\u96c6\u5408\u6709\u4e00\u4e2a\u7a7a\u6392\u5217\uff0c\u53d6\u4e58\u6cd5\u5355\u4f4d\u5143\u624d\u80fd\u8ba9\u7ec4\u5408\u89c4\u5219\u5728\u8fb9\u754c\u4fdd\u6301\u4e00\u81f4\u3002","_wpcom_ai_launchpad_first_post":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[787297218],"tags":[787297288,787297289,787300794,787300793],"class_list":["post-20461","post","type-post","status-publish","format-standard","hentry","category-daily-maths-physics-chemistry","tag-combinatorics","tag-combinatorics-zh","tag-factorials-zh","tag-factorials",""],"translatepress_titles":{"en_AU":"Why Does 0! 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