<story><title>Gödel’s first incompleteness theorem – an interactive tutorial</title><url>https://tigyog.app/d/H7XOvXvC_x/r/goedel-s-first-incompleteness-theorem</url></story><parent_chain></parent_chain><comment><author>dvt</author><text>Cool page, though the Halting Problem brings with it a &lt;i&gt;lot&lt;/i&gt; of stuff, so using it to prove Godel&amp;#x27;s first incompleteness theorem is (imo) a bit like cheating. I&amp;#x27;ve proven it before using diagonalization on my blog (but also using concepts like computability for free). At the end of the day, using these ideas, you get the Curry–Howard correspondence for free (which, again, is a bit like cheating).&lt;p&gt;&amp;gt; Gödel’s original proof was slightly stronger&lt;p&gt;Technically speaking, a &lt;i&gt;lot&lt;/i&gt; stronger. Proving Godel&amp;#x27;s first incompleteness theorem (don&amp;#x27;t even get me started on the second) from first principles is actually &lt;i&gt;much&lt;/i&gt; more involved; and &lt;i&gt;certainly&lt;/i&gt; more difficult to make it intelligible for non-logicians.</text></comment>
<story><title>Gödel’s first incompleteness theorem – an interactive tutorial</title><url>https://tigyog.app/d/H7XOvXvC_x/r/goedel-s-first-incompleteness-theorem</url></story><parent_chain></parent_chain><comment><author>aljgz</author><text>A math prof had a brilliant blog and one of the subjects he covered was Gödel&amp;#x27;s incomepleteness theorems. I really loved his style (and his wife&amp;#x27;s illustrations). Too bad he stopped posting.&lt;p&gt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;infinityplusonemath.wordpress.com&amp;#x2F;2017&amp;#x2F;07&amp;#x2F;22&amp;#x2F;kurt-godels-story&amp;#x2F;&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;infinityplusonemath.wordpress.com&amp;#x2F;2017&amp;#x2F;07&amp;#x2F;22&amp;#x2F;kurt-go...&lt;/a&gt;&lt;p&gt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;infinityplusonemath.wordpress.com&amp;#x2F;2017&amp;#x2F;08&amp;#x2F;04&amp;#x2F;godels-incompleteness-theorems&amp;#x2F;&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;infinityplusonemath.wordpress.com&amp;#x2F;2017&amp;#x2F;08&amp;#x2F;04&amp;#x2F;godels-...&lt;/a&gt;&lt;p&gt;&lt;a href=&quot;https:&amp;#x2F;&amp;#x2F;infinityplusonemath.wordpress.com&amp;#x2F;2017&amp;#x2F;09&amp;#x2F;04&amp;#x2F;how-godel-proved-maths-inherent-limitations&amp;#x2F;&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;infinityplusonemath.wordpress.com&amp;#x2F;2017&amp;#x2F;09&amp;#x2F;04&amp;#x2F;how-god...&lt;/a&gt;</text></comment>