User blog comment:B1mb0w/J Function Sandpit J 4/@comment-27173506-20160205161632

You have a mistake in your FSes. \(\varphi(1,0,0)\) does not equal \(\text{sup} \lbrace \varphi(1,0), \varphi(2,0) , \varphi(3,0) \cdots \rbrace\), that is merely \(\varphi(\omega,0)\). \(\varphi(1,0,0)=\text{sup} \lbrace \varphi(1,0), \varphi(\varphi(1,0),0) , \varphi(\varphi(\varphi(1,0),0),0) \cdots \rbrace\). You make similar mistakes throughout your blog post.