tag:blogger.com,1999:blog-33803276.post3263471355646412879..comments2023-11-02T12:07:59.900-04:00Comments on The Disparate Notions of a Lowly Mathematician: Peano's Axioms Part II: Orderability and CodeJoe Fredettehttp://www.blogger.com/profile/07170469679136904832noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-33803276.post-49227018300722108492007-07-26T01:38:00.000-04:002007-07-26T01:38:00.000-04:00Oh crap, your absolutely correct, fritz, thanks fo...Oh crap, your absolutely correct, fritz, thanks for catching that. I did quote directly from wikipedia. I've never been able to remember the Induction axiom correctly off the top of my head. It's one of those "I know what it is, just not how to say it." Things. Should be fixed now.<BR/><BR/>Thanks againJoe Fredettehttps://www.blogger.com/profile/07170469679136904832noreply@blogger.comtag:blogger.com,1999:blog-33803276.post-67937761316622664102007-07-24T03:18:00.000-04:002007-07-24T03:18:00.000-04:00Among other things, you have used 0 as your base c...Among other things, you have used 0 as your base case in the first few axioms, then switched to 1 for the induction axiom. (You quoted Wikpedia, and I think its definition uses the number theorists' convention of excluding 0 from the naturals, as I understand Peano did. But CS/logic types in this day and age tend to include 0.)Fritz Ruehrhttps://www.blogger.com/profile/07287120856377258774noreply@blogger.comtag:blogger.com,1999:blog-33803276.post-51584081576594875472007-07-12T12:50:00.000-04:002007-07-12T12:50:00.000-04:00it probably is, I was doing it from memory. I'll d...it probably is, I was doing it from memory. I'll dig up a better definition. I was writing the post while offline, so I didn't have access to my online notes.Joe Fredettehttps://www.blogger.com/profile/07170469679136904832noreply@blogger.comtag:blogger.com,1999:blog-33803276.post-53202150357739771562007-07-12T06:01:00.000-04:002007-07-12T06:01:00.000-04:00Your induction axiom looks slightly wrong.Your induction axiom looks slightly wrong.augustsshttps://www.blogger.com/profile/07327620522294658036noreply@blogger.com