<![CDATA[Math Is Fun Forum / Induction]]>2013-02-18T12:41:08ZFluxBBhttp://www.mathisfunforum.com/viewtopic.php?id=19004<![CDATA[Re: Induction]]>It looks fine to me. However proving stuff about integers is usually much more straightforward: first prove that the property holds for all non-negative integers, then show that it also holds for where is a non-negative integer.]]>http://www.mathisfunforum.com/profile.php?id=502822013-02-18T12:41:08Zhttp://www.mathisfunforum.com/viewtopic.php?pid=254241#p254241<![CDATA[Re: Induction]]>So,can this axiom be used to prove stuff for integers?]]>http://www.mathisfunforum.com/profile.php?id=1983882013-02-18T12:33:22Zhttp://www.mathisfunforum.com/viewtopic.php?pid=254240#p254240<![CDATA[Re: Induction]]>anonimnystefy wrote:

I think (c) is unneccessary there, and the rest just represents the axiom of induction.

It is necessary. This is the induction law for , not .]]>http://www.mathisfunforum.com/profile.php?id=502822013-02-18T11:26:02Zhttp://www.mathisfunforum.com/viewtopic.php?pid=254229#p254229<![CDATA[Re: Induction]]>By (c) i stated that -1,-2,-3,-4,... are in S,the general axiom doesn't state that.]]>http://www.mathisfunforum.com/profile.php?id=1983882013-02-18T02:52:20Zhttp://www.mathisfunforum.com/viewtopic.php?pid=254179#p254179<![CDATA[Re: Induction]]>I think (c) is unneccessary there, and the rest just represents the axiom of induction.]]>http://www.mathisfunforum.com/profile.php?id=1187862013-02-18T02:25:46Zhttp://www.mathisfunforum.com/viewtopic.php?pid=254176#p254176<![CDATA[Induction]]>Hi, I think i have found a way to use induction for integer set too (don't know if it was discovered before this post) by extending the axiom of induction we get "if S is a subset of Z and (a) 0 belongs to S,(b) for n belonging to S (n+1) belongs to S,(c)for n belonging to S (n-1) belongs to S ,then S=Z." if I'm wrong I hope others will correct me.]]>http://www.mathisfunforum.com/profile.php?id=1983882013-02-18T02:14:37Zhttp://www.mathisfunforum.com/viewtopic.php?pid=254175#p254175