tag:blogger.com,1999:blog-6839602.post6770736201775450370..comments2022-04-10T12:51:16.973-07:00Comments on Everyone Else is Crazy: Countable Ordinals in HaskellJim Applehttp://www.blogger.com/profile/11080395413026172939noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-6839602.post-31843585574161425092015-09-09T18:53:08.019-07:002015-09-09T18:53:08.019-07:00This comment has been removed by a blog administrator.Anonymoushttps://www.blogger.com/profile/07720547920308398294noreply@blogger.comtag:blogger.com,1999:blog-6839602.post-62793390880710668442015-07-15T22:55:36.086-07:002015-07-15T22:55:36.086-07:00This comment has been removed by a blog administrator.Anonymoushttps://www.blogger.com/profile/11708398102654526740noreply@blogger.comtag:blogger.com,1999:blog-6839602.post-92074584466129977082015-03-13T19:00:31.752-07:002015-03-13T19:00:31.752-07:00This comment has been removed by a blog administrator.andrea chiuhttps://www.blogger.com/profile/04035532519352427999noreply@blogger.comtag:blogger.com,1999:blog-6839602.post-61417386468535014912008-02-06T02:29:00.000-08:002008-02-06T02:29:00.000-08:00Hi, it is me again. I wrote this for jared and any...Hi, it is me again. I wrote <A HREF="http://math.andrej.com/2008/02/06/representations-of-uncomputable-and-uncountable-sets/" REL="nofollow">this</A> for jared and anyone else that might be interested. As my post explains, in the cae of ordinals, the cruicial question is: which operations on ordinals should be computable. For example, is the order relation computable for your representation?Unknownhttps://www.blogger.com/profile/07919699809378198245noreply@blogger.comtag:blogger.com,1999:blog-6839602.post-37312001155423134042008-02-06T00:02:00.000-08:002008-02-06T00:02:00.000-08:00The V=L axiom has little to do with what you are t...The V=L axiom has little to do with what you are talking about. You make it sound as if V=L means that "all is countable". In fact, even if you assume V=L there will still be plenty of very large sets around.<BR/><BR/>Also, it is a bit inaccurate to say that you are representing all countable ordinals. At best you are representing ordinals below the <A HREF="http://en.wikipedia.org/wiki/Proof-theoretic_ordinal" REL="nofollow">Church-Kleene ordinal</A>.<BR/><BR/>An Jared said that it is "impossible for a computer to represent uncountable sets". This is false, see e.g., Klaus Weihrauch's book <A HREF="http://books.google.si/books?id=OPolVWVFDJYC&dq=klaus+weihrauch+computable+analysis&pg=PP1&ots=_QfWckVnYF&sig=9rv8zPvf6bqYLfk-ESifJMVVsOU&hl=en&prev=http://www.google.si/search?q=klaus+weihrauch+computable+analysis&ie=utf-8&oe=utf-8&rls=com.ubuntu:en-US:official&client=firefox-a&sa=X&oi=print&ct=title&cad=one-book-with-thumbnail" REL="nofollow">"Computable Analysis"</A> for an explanation about why this is not the case. Actually, I am going to go now and write a blog post about this, since "non-professionals" seem to be a bit misguided about this.Unknownhttps://www.blogger.com/profile/07919699809378198245noreply@blogger.comtag:blogger.com,1999:blog-6839602.post-18553434578632255932008-02-05T19:39:00.000-08:002008-02-05T19:39:00.000-08:00It is indeed impossible for a computer to represen...It is indeed impossible for a computer to represent an uncountable set. Such a representation would be a function from the natural numbers to the set, which would constitute a proof that the set was countable.Unknownhttps://www.blogger.com/profile/06250182324070402100noreply@blogger.com