{"action":"created","issue":{"url":"https://api.github.com/repos/kelseyhightower/nocode/issues/2343","repository_url":"https://api.github.com/repos/kelseyhightower/nocode","labels_url":"https://api.github.com/repos/kelseyhightower/nocode/issues/2343/labels{/name}","comments_url":"https://api.github.com/repos/kelseyhightower/nocode/issues/2343/comments","events_url":"https://api.github.com/repos/kelseyhightower/nocode/issues/2343/events","html_url":"https://github.com/kelseyhightower/nocode/issues/2343","id":321485657,"number":2343,"title":"1+1=2?","user":{"login":"snowpine","id":612599,"avatar_url":"https://avatars0.githubusercontent.com/u/612599?v=4","gravatar_id":"","url":"https://api.github.com/users/snowpine","html_url":"https://github.com/snowpine","followers_url":"https://api.github.com/users/snowpine/followers","following_url":"https://api.github.com/users/snowpine/following{/other_user}","gists_url":"https://api.github.com/users/snowpine/gists{/gist_id}","starred_url":"https://api.github.com/users/snowpine/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/snowpine/subscriptions","organizations_url":"https://api.github.com/users/snowpine/orgs","repos_url":"https://api.github.com/users/snowpine/repos","events_url":"https://api.github.com/users/snowpine/events{/privacy}","received_events_url":"https://api.github.com/users/snowpine/received_events","type":"User","site_admin":false},"labels":[],"state":"open","locked":false,"assignee":null,"assignees":[],"milestone":null,"comments":4,"created_at":"2018-05-09T08:54:59Z","updated_at":"2018-05-14T16:25:25Z","closed_at":null,"author_association":"NONE","body":"https://www.zhihu.com/question/23866990\r\n\r\n<div class=\"RichContent-inner\"><span class=\"RichText CopyrightRichText-richText\" itemprop=\"text\"><p><strong>1 引言</strong><br></p><p>“为什么1+1=2？”，我眉头紧皱，抚案沉思，答案涌上心头，“存在即合理”，不叫1+1=2，也会叫a+b=c，到时候就会有人来问“为什么a+b=c”。</p><p>学了数学之后才发现自己太naive，纯粹属于“书读得太少，却想得太多”。</p><p><strong>2 自然数的构造</strong></p><p>数学是数学家构造出来的一个世界，那么自然数的构造就是数学世界的开天辟地。</p><p><strong>2.1 选择</strong></p><p>我们先放空自己，想象在连空间、时间都一无所有的数学世界里（空间、时间还要在自然数之后才能被创造出来），我们应该怎么去创造自然数？</p><p>自然数会不会是这样的：</p><figure><noscript><img src=\"https://pic2.zhimg.com/50/v2-11e72f5f212305092ba7df0e4d4c3978_hd.jpg\" data-rawwidth=\"651\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"651\" data-original=\"https://pic2.zhimg.com/v2-11e72f5f212305092ba7df0e4d4c3978_r.jpg\"></noscript><img src=\"https://pic2.zhimg.com/80/v2-11e72f5f212305092ba7df0e4d4c3978_hd.jpg\" data-rawwidth=\"651\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"651\" data-original=\"https://pic2.zhimg.com/v2-11e72f5f212305092ba7df0e4d4c3978_r.jpg\" data-actualsrc=\"https://pic2.zhimg.com/50/v2-11e72f5f212305092ba7df0e4d4c3978_hd.jpg\"></figure><p></p><p>或者是这样的：</p><figure><noscript><img src=\"https://pic2.zhimg.com/50/v2-2303b0a398c73e2ebf436a203c704c27_hd.jpg\" data-rawwidth=\"804\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"804\" data-original=\"https://pic2.zhimg.com/v2-2303b0a398c73e2ebf436a203c704c27_r.jpg\"></noscript><img src=\"https://pic2.zhimg.com/80/v2-2303b0a398c73e2ebf436a203c704c27_hd.jpg\" data-rawwidth=\"804\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"804\" data-original=\"https://pic2.zhimg.com/v2-2303b0a398c73e2ebf436a203c704c27_r.jpg\" data-actualsrc=\"https://pic2.zhimg.com/50/v2-2303b0a398c73e2ebf436a203c704c27_hd.jpg\"></figure><p></p><p>甚至这样：</p><figure><noscript><img src=\"https://pic2.zhimg.com/50/v2-5727e7581034b61225598132b168b6d7_hd.jpg\" data-rawwidth=\"633\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"633\" data-original=\"https://pic2.zhimg.com/v2-5727e7581034b61225598132b168b6d7_r.jpg\"></noscript><img src=\"https://pic2.zhimg.com/80/v2-5727e7581034b61225598132b168b6d7_hd.jpg\" data-rawwidth=\"633\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"633\" data-original=\"https://pic2.zhimg.com/v2-5727e7581034b61225598132b168b6d7_r.jpg\" data-actualsrc=\"https://pic2.zhimg.com/50/v2-5727e7581034b61225598132b168b6d7_hd.jpg\"></figure><p></p><p>选择不同的自然数体系，那么数学世界会完全不同，大家也知道最后我们做了这个选择：</p><figure><noscript><img src=\"https://pic1.zhimg.com/50/v2-222a162e75366a6ae9b130bdaf2f67d6_hd.jpg\" data-rawwidth=\"848\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"848\" data-original=\"https://pic1.zhimg.com/v2-222a162e75366a6ae9b130bdaf2f67d6_r.jpg\"></noscript><img src=\"https://pic1.zhimg.com/80/v2-222a162e75366a6ae9b130bdaf2f67d6_hd.jpg\" data-rawwidth=\"848\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"848\" data-original=\"https://pic1.zhimg.com/v2-222a162e75366a6ae9b130bdaf2f67d6_r.jpg\" data-actualsrc=\"https://pic1.zhimg.com/50/v2-222a162e75366a6ae9b130bdaf2f67d6_hd.jpg\"></figure><p></p><p>这个选择是自然而然做出来的，是经过历史考验的，所以我们称之为“自然数”。</p><p>你猜猜，外星人会不会做出和我们一样的选择？至少目前看来地球上各个独立发展的文明基本都做出了一样的选择。</p><p><strong>2.2 皮亚诺公理</strong></p><p>意大利数学家皮亚诺用公理把自然数安放在了数学世界里面。</p><blockquote><b>公理1：0是自然数。</b></blockquote><p>空旷的世界有了第一个孤独的元素：</p><figure><noscript><img src=\"https://pic1.zhimg.com/50/v2-3ca579ef44c9a19caa74d091614406a8_hd.jpg\" data-rawwidth=\"1059\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"1059\" data-original=\"https://pic1.zhimg.com/v2-3ca579ef44c9a19caa74d091614406a8_r.jpg\"></noscript><img src=\"https://pic1.zhimg.com/80/v2-3ca579ef44c9a19caa74d091614406a8_hd.jpg\" data-rawwidth=\"1059\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"1059\" data-original=\"https://pic1.zhimg.com/v2-3ca579ef44c9a19caa74d091614406a8_r.jpg\" data-actualsrc=\"https://pic1.zhimg.com/50/v2-3ca579ef44c9a19caa74d091614406a8_hd.jpg\"></figure><p></p><p>这就是产生整个宇宙的奇点。上帝创世的第一天是不是就是放置下了自然数0？</p><p>然后奇点0的大爆炸应该是什么样子的？</p><figure><noscript><img src=\"https://pic3.zhimg.com/50/v2-101f1682628af51684782fbed9f6b27b_hd.jpg\" data-rawwidth=\"724\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"724\" data-original=\"https://pic3.zhimg.com/v2-101f1682628af51684782fbed9f6b27b_r.jpg\"></noscript><img src=\"https://pic3.zhimg.com/80/v2-101f1682628af51684782fbed9f6b27b_hd.jpg\" data-rawwidth=\"724\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"724\" data-original=\"https://pic3.zhimg.com/v2-101f1682628af51684782fbed9f6b27b_r.jpg\" data-actualsrc=\"https://pic3.zhimg.com/50/v2-101f1682628af51684782fbed9f6b27b_hd.jpg\"></figure><p></p><blockquote><b>公理2：每一个确定的自然数 <img src=\"https://www.zhihu.com/equation?tex=a\" alt=\"a\" eeimg=\"1\"> ，都有一个确定的后继数 <img src=\"https://www.zhihu.com/equation?tex=a%27\" alt=\"a'\" eeimg=\"1\"> , <img src=\"https://www.zhihu.com/equation?tex=a%27\" alt=\"a'\" eeimg=\"1\"> 也是自然数。</b></blockquote><p>这个公理做出了选择：</p><figure><noscript><img src=\"https://pic4.zhimg.com/50/v2-2be3f0b932738b51f48542d90db27f8e_hd.jpg\" data-rawwidth=\"724\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"724\" data-original=\"https://pic4.zhimg.com/v2-2be3f0b932738b51f48542d90db27f8e_r.jpg\"></noscript><img src=\"https://pic4.zhimg.com/80/v2-2be3f0b932738b51f48542d90db27f8e_hd.jpg\" data-rawwidth=\"724\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"724\" data-original=\"https://pic4.zhimg.com/v2-2be3f0b932738b51f48542d90db27f8e_r.jpg\" data-actualsrc=\"https://pic4.zhimg.com/50/v2-2be3f0b932738b51f48542d90db27f8e_hd.jpg\"></figure><p></p><p>为了避免太过于“迂腐”，“后继数”这个词未加定义的就使用了。</p><p>基本上雏形是有了：</p><figure><noscript><img src=\"https://pic3.zhimg.com/50/v2-69c3fd1e67f2738c08a5ff72f539876a_hd.jpg\" data-rawwidth=\"686\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"686\" data-original=\"https://pic3.zhimg.com/v2-69c3fd1e67f2738c08a5ff72f539876a_r.jpg\"></noscript><img src=\"https://pic3.zhimg.com/80/v2-69c3fd1e67f2738c08a5ff72f539876a_hd.jpg\" data-rawwidth=\"686\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"686\" data-original=\"https://pic3.zhimg.com/v2-69c3fd1e67f2738c08a5ff72f539876a_r.jpg\" data-actualsrc=\"https://pic3.zhimg.com/50/v2-69c3fd1e67f2738c08a5ff72f539876a_hd.jpg\"></figure><p></p><p>但是还是可能长成这种造型：</p><figure><noscript><img src=\"https://pic2.zhimg.com/50/v2-ae1e890cc9cf2b05470efb17d4bf2be1_hd.jpg\" data-rawwidth=\"551\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"551\" data-original=\"https://pic2.zhimg.com/v2-ae1e890cc9cf2b05470efb17d4bf2be1_r.jpg\"></noscript><img src=\"https://pic2.zhimg.com/80/v2-ae1e890cc9cf2b05470efb17d4bf2be1_hd.jpg\" data-rawwidth=\"551\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"551\" data-original=\"https://pic2.zhimg.com/v2-ae1e890cc9cf2b05470efb17d4bf2be1_r.jpg\" data-actualsrc=\"https://pic2.zhimg.com/50/v2-ae1e890cc9cf2b05470efb17d4bf2be1_hd.jpg\"></figure><p></p><blockquote><b>公理3：0不是任何自然数的后继数。</b></blockquote><p>这条公理直接把上面的情况给毙了：</p><figure><noscript><img src=\"https://pic2.zhimg.com/50/v2-80b003a87cc243d5bacea0f779cba966_hd.jpg\" data-rawwidth=\"551\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"551\" data-original=\"https://pic2.zhimg.com/v2-80b003a87cc243d5bacea0f779cba966_r.jpg\"></noscript><img src=\"https://pic2.zhimg.com/80/v2-80b003a87cc243d5bacea0f779cba966_hd.jpg\" data-rawwidth=\"551\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"551\" data-original=\"https://pic2.zhimg.com/v2-80b003a87cc243d5bacea0f779cba966_r.jpg\" data-actualsrc=\"https://pic2.zhimg.com/50/v2-80b003a87cc243d5bacea0f779cba966_hd.jpg\"></figure><p></p><p>同时这个公理也说明了0必须也只能是自然数的第一个数。</p><p>但是还是可能长成这种造型（真多事啊）：</p><figure><noscript><img src=\"https://pic1.zhimg.com/50/v2-851856fe36b69435cc21d682d9618caa_hd.jpg\" data-rawwidth=\"610\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"610\" data-original=\"https://pic1.zhimg.com/v2-851856fe36b69435cc21d682d9618caa_r.jpg\"></noscript><img src=\"https://pic1.zhimg.com/80/v2-851856fe36b69435cc21d682d9618caa_hd.jpg\" data-rawwidth=\"610\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"610\" data-original=\"https://pic1.zhimg.com/v2-851856fe36b69435cc21d682d9618caa_r.jpg\" data-actualsrc=\"https://pic1.zhimg.com/50/v2-851856fe36b69435cc21d682d9618caa_hd.jpg\"></figure><p></p><blockquote><b>公理4：不同的自然数有不同的后继数。</b></blockquote><p>这个公理可以避免上面的情况出现：</p><figure><noscript><img src=\"https://pic3.zhimg.com/50/v2-c67dc2d00298bb3fef5fffba82640323_hd.jpg\" data-rawwidth=\"610\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"610\" data-original=\"https://pic3.zhimg.com/v2-c67dc2d00298bb3fef5fffba82640323_r.jpg\"></noscript><img src=\"https://pic3.zhimg.com/80/v2-c67dc2d00298bb3fef5fffba82640323_hd.jpg\" data-rawwidth=\"610\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"610\" data-original=\"https://pic3.zhimg.com/v2-c67dc2d00298bb3fef5fffba82640323_r.jpg\" data-actualsrc=\"https://pic3.zhimg.com/50/v2-c67dc2d00298bb3fef5fffba82640323_hd.jpg\"></figure><p></p><p>我们终于可以一个数一个数的数下去了。</p><p>但是现在就全是自然数了吗？这样行不行：</p><figure><noscript><img src=\"https://pic4.zhimg.com/50/v2-40b299ff65237241aba8a1f36090071b_hd.jpg\" data-rawwidth=\"848\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"848\" data-original=\"https://pic4.zhimg.com/v2-40b299ff65237241aba8a1f36090071b_r.jpg\"></noscript><img src=\"https://pic4.zhimg.com/80/v2-40b299ff65237241aba8a1f36090071b_hd.jpg\" data-rawwidth=\"848\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"848\" data-original=\"https://pic4.zhimg.com/v2-40b299ff65237241aba8a1f36090071b_r.jpg\" data-actualsrc=\"https://pic4.zhimg.com/50/v2-40b299ff65237241aba8a1f36090071b_hd.jpg\"></figure><p></p><p>这个数系：</p><p>｛0，0.5，1，1.5，2，3……｝</p><p>这个数系满足公理1-4：</p><ul><li><p>0是自然数。</p></li><li><p>每一个确定的自然数 <img src=\"https://www.zhihu.com/equation?tex=a\" alt=\"a\" eeimg=\"1\"> 都有确定的后继数 <img src=\"https://www.zhihu.com/equation?tex=a%27\" alt=\"a'\" eeimg=\"1\"> ， <img src=\"https://www.zhihu.com/equation?tex=a%27\" alt=\"a'\" eeimg=\"1\"> 也是自然数。</p></li><li><p>0不是任何自然数的后继数。</p></li><li><p>不同的自然数的有不同的后继数。</p></li></ul><p>但是0.5这样的数不是自然数啊，我们一定要干掉它。</p><p>于是又加上一个公理：</p><blockquote><b>公理5：任意关于自然数的性质，如果证明了它对自然数0是对的，又假定它对自然数n为真时，可以证明它对 <img src=\"https://www.zhihu.com/equation?tex=n%27\" alt=\"n'\" eeimg=\"1\"> 为真，那么命题对所有自然数都真。</b></blockquote><p>这里有点绕，自然数都没有构造完，自然没有办法定义具体的自然数性质，这个公理就是说当以后我们定义了一个自然数的性质，自然数都要满足。</p><p>并且，这个公理就是数学归纳法！</p><p>感受一下这个命题:</p><blockquote><b><img src=\"https://www.zhihu.com/equation?tex=n\" alt=\"n\" eeimg=\"1\"> 是自然数，那么 <img src=\"https://www.zhihu.com/equation?tex=n%5E2\" alt=\"n^2\" eeimg=\"1\"> 是自然数，并且 <img src=\"https://www.zhihu.com/equation?tex=n%5E2\" alt=\"n^2\" eeimg=\"1\"> 大于等于 <img src=\"https://www.zhihu.com/equation?tex=n\" alt=\"n\" eeimg=\"1\"> 。</b></blockquote><p>这个是我们的自然数的一个性质， <img src=\"https://www.zhihu.com/equation?tex=0.5%5E2%3D0.25\" alt=\"0.5^2=0.25\" eeimg=\"1\"> ， <img src=\"https://www.zhihu.com/equation?tex=0.25%3C0.5\" alt=\"0.25<0.5\" eeimg=\"1\"> ，不满足这个性质，干掉：<br></p><figure><noscript><img src=\"https://pic4.zhimg.com/50/v2-059ae59e14d1909823431f3032e0b9b4_hd.jpg\" data-rawwidth=\"848\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"848\" data-original=\"https://pic4.zhimg.com/v2-059ae59e14d1909823431f3032e0b9b4_r.jpg\"></noscript><img src=\"https://pic4.zhimg.com/80/v2-059ae59e14d1909823431f3032e0b9b4_hd.jpg\" data-rawwidth=\"848\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"848\" data-original=\"https://pic4.zhimg.com/v2-059ae59e14d1909823431f3032e0b9b4_r.jpg\" data-actualsrc=\"https://pic4.zhimg.com/50/v2-059ae59e14d1909823431f3032e0b9b4_hd.jpg\"></figure><p></p><p>上面给出了一个通俗的说明，下面为有疑问的朋友进行更严格一点的说明，一般来说会有如下疑问：</p><ul><li><p>0.5没有定义，怎么就出现了？</p></li><li><p>0.5不过就是一个命名而已，我可以规定0.5也是自然数，0.25也是自然数，并且0.25排在0.5的后面。</p></li></ul><p>我们从这个角度来看待公理5：公理5就是数学归纳法，用数学归纳法可以证明的定理，如果某个数不符合此定理，则一定不为自然数。</p><p>对于0.5的出现这么来考虑，我们先定义了自然数集，然后又用自然数集扩张为有理数集，然后在有理数中挑一个数，比如说0.5，因为自然数本身是有理数的子集，所以我并不清楚0.5是不是自然数，但是我这么检验，其平方为0.25，对于自然数不可能平方小于自身，所以它不是自然数。</p><p>公理5也将在接下来的加法定义中发挥作用。</p><p><strong>2.3 命名</strong></p><p>皮亚诺公理定义了什么是自然数：他们是这样｛ <img src=\"https://www.zhihu.com/equation?tex=0%2C0%27%2C0%27%27%2C0%27%27%27%2C0%27%27%27%27%2C%5Ccdots+\" alt=\"0,0',0'',0''',0'''',\\cdots \" eeimg=\"1\"> ｝，这样称呼起来太麻烦了，历史上早就把它们的名字准备好了，就是｛ <img src=\"https://www.zhihu.com/equation?tex=0%2C1%2C2%2C3%2C4%2C%5Ccdots+\" alt=\"0,1,2,3,4,\\cdots \" eeimg=\"1\"> ｝：</p><figure><noscript><img src=\"https://pic4.zhimg.com/50/v2-350423427aafe7bce5c9a833a30e7562_hd.jpg\" data-rawwidth=\"848\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"848\" data-original=\"https://pic4.zhimg.com/v2-350423427aafe7bce5c9a833a30e7562_r.jpg\"></noscript><img src=\"https://pic4.zhimg.com/80/v2-350423427aafe7bce5c9a833a30e7562_hd.jpg\" data-rawwidth=\"848\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"848\" data-original=\"https://pic4.zhimg.com/v2-350423427aafe7bce5c9a833a30e7562_r.jpg\" data-actualsrc=\"https://pic4.zhimg.com/50/v2-350423427aafe7bce5c9a833a30e7562_hd.jpg\"></figure><p></p><p>当然也可以叫别的，比如英语里面就是one、two、three、four、 <img src=\"https://www.zhihu.com/equation?tex=%5Ccdots+\" alt=\"\\cdots \" eeimg=\"1\"> 。</p><p><strong>3 加法</strong></p><p>只有自然数的数学世界仍然死气沉沉，增加的加法让数字与数字之间开始有了化学反应：</p><figure><noscript><img src=\"https://pic4.zhimg.com/50/v2-261e79bc96e3800c0326919b741889b6_hd.jpg\" data-rawwidth=\"848\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"848\" data-original=\"https://pic4.zhimg.com/v2-261e79bc96e3800c0326919b741889b6_r.jpg\"></noscript><img src=\"https://pic4.zhimg.com/80/v2-261e79bc96e3800c0326919b741889b6_hd.jpg\" data-rawwidth=\"848\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"848\" data-original=\"https://pic4.zhimg.com/v2-261e79bc96e3800c0326919b741889b6_r.jpg\" data-actualsrc=\"https://pic4.zhimg.com/50/v2-261e79bc96e3800c0326919b741889b6_hd.jpg\"></figure><p></p><blockquote><b>定义自然数的加法：设m是自然数，我们定义0+m:=m.如果定义m加上n:=m+n,那么<img src=\"https://www.zhihu.com/equation?tex=m%2Bn%27%3A%3D%28m%2Bn%29%27\" alt=\"m+n':=(m+n)'\" eeimg=\"1\"></b></blockquote><p>要证明 <img src=\"https://www.zhihu.com/equation?tex=%28m%2Bn%29%27\" alt=\"(m+n)'\" eeimg=\"1\"> 也是自然数，就需要用到公理5。<br></p><p>我们来计算一下3+2的值：</p><p>计算 <img src=\"https://www.zhihu.com/equation?tex=3%2B2\" alt=\"3+2\" eeimg=\"1\"> 的值就是计算 <img src=\"https://www.zhihu.com/equation?tex=0%27%27%27%2B0%27%27\" alt=\"0'''+0''\" eeimg=\"1\"> 的值。</p><p>所以有 <img src=\"https://www.zhihu.com/equation?tex=3%2B2%3D0%27%27%27%2B0%27%27%3D%280%27%27%27%29%27%27%3D0%27%27%27%27%27%3D5\" alt=\"3+2=0'''+0''=(0''')''=0'''''=5\" eeimg=\"1\"> 。</p><p>加法就像这样：</p><figure><noscript><img src=\"https://pic3.zhimg.com/50/v2-a9a6add7b0314d8c10fae6676fd04b55_hd.jpg\" data-rawwidth=\"629\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"629\" data-original=\"https://pic3.zhimg.com/v2-a9a6add7b0314d8c10fae6676fd04b55_r.jpg\"></noscript><img src=\"https://pic3.zhimg.com/80/v2-a9a6add7b0314d8c10fae6676fd04b55_hd.jpg\" data-rawwidth=\"629\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"629\" data-original=\"https://pic3.zhimg.com/v2-a9a6add7b0314d8c10fae6676fd04b55_r.jpg\" data-actualsrc=\"https://pic3.zhimg.com/50/v2-a9a6add7b0314d8c10fae6676fd04b55_hd.jpg\"></figure><p></p><p>现在我们终于可以来解答1+1为什么等于2：</p><figure><noscript><img src=\"https://pic3.zhimg.com/50/v2-a7d18c7250c4687eb8dc1db1e5f8068b_hd.jpg\" data-rawwidth=\"533\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"533\" data-original=\"https://pic3.zhimg.com/v2-a7d18c7250c4687eb8dc1db1e5f8068b_r.jpg\"></noscript><img src=\"https://pic3.zhimg.com/80/v2-a7d18c7250c4687eb8dc1db1e5f8068b_hd.jpg\" data-rawwidth=\"533\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"533\" data-original=\"https://pic3.zhimg.com/v2-a7d18c7250c4687eb8dc1db1e5f8068b_r.jpg\" data-actualsrc=\"https://pic3.zhimg.com/50/v2-a7d18c7250c4687eb8dc1db1e5f8068b_hd.jpg\"></figure><p></p><p><strong>4 大爆炸的继续</strong></p><p>自然数和加法是数学世界的根基（当然还有集合论等，忍不住还是严谨一下），在这个基础上数学世界越来越辉煌，这就是为什么需要证明“1+1=2”：：</p><figure><noscript><img src=\"https://pic4.zhimg.com/50/v2-66af4634d467620634cb02957b4a788c_hd.jpg\" data-rawwidth=\"868\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"868\" data-original=\"https://pic4.zhimg.com/v2-66af4634d467620634cb02957b4a788c_r.jpg\"></noscript><img src=\"https://pic4.zhimg.com/80/v2-66af4634d467620634cb02957b4a788c_hd.jpg\" data-rawwidth=\"868\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"868\" data-original=\"https://pic4.zhimg.com/v2-66af4634d467620634cb02957b4a788c_r.jpg\" data-actualsrc=\"https://pic4.zhimg.com/50/v2-66af4634d467620634cb02957b4a788c_hd.jpg\"></figure><p></p><p><strong>5 思考</strong></p><p>为什么数轴是直的， 而不是长成这样：</p><figure><noscript><img src=\"https://pic3.zhimg.com/50/v2-a4035413475923532b480aa9bbf263a4_hd.jpg\" data-rawwidth=\"473\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb\" width=\"473\" data-original=\"https://pic3.zhimg.com/v2-a4035413475923532b480aa9bbf263a4_r.jpg\"></noscript><img src=\"https://pic3.zhimg.com/80/v2-a4035413475923532b480aa9bbf263a4_hd.jpg\" data-rawwidth=\"473\" data-rawheight=\"402\" class=\"origin_image zh-lightbox-thumb lazy\" width=\"473\" data-original=\"https://pic3.zhimg.com/v2-a4035413475923532b480aa9bbf263a4_r.jpg\" data-actualsrc=\"https://pic3.zhimg.com/50/v2-a4035413475923532b480aa9bbf263a4_hd.jpg\"></figure><br><p></p><p>这倒没什么正确答案，不过确实有一些数学原因。</p><p>思考是数学真正的乐趣。</p><p>参考文献：《陶哲轩实分析》</p></span></div>"},"comment":{"url":"https://api.github.com/repos/kelseyhightower/nocode/issues/comments/388878168","html_url":"https://github.com/kelseyhightower/nocode/issues/2343#issuecomment-388878168","issue_url":"https://api.github.com/repos/kelseyhightower/nocode/issues/2343","id":388878168,"user":{"login":"deepserket","id":22613202,"avatar_url":"https://avatars0.githubusercontent.com/u/22613202?v=4","gravatar_id":"","url":"https://api.github.com/users/deepserket","html_url":"https://github.com/deepserket","followers_url":"https://api.github.com/users/deepserket/followers","following_url":"https://api.github.com/users/deepserket/following{/other_user}","gists_url":"https://api.github.com/users/deepserket/gists{/gist_id}","starred_url":"https://api.github.com/users/deepserket/starred{/owner}{/repo}","subscriptions_url":"https://api.github.com/users/deepserket/subscriptions","organizations_url":"https://api.github.com/users/deepserket/orgs","repos_url":"https://api.github.com/users/deepserket/repos","events_url":"https://api.github.com/users/deepserket/events{/privacy}","received_events_url":"https://api.github.com/users/deepserket/received_events","type":"User","site_admin":false},"created_at":"2018-05-14T16:25:25Z","updated_at":"2018-05-14T16:25:25Z","author_association":"NONE","body":"thit was a great trip, thanks @snowpine"}}
{"actor":{"display_login":"deepserket"}}