Talk:Element of Minimal Infinite Successor Set is Transitive Set

This proof does not show that the set of all natural numbers is itself transitive. It shows that each element of $\N$ is transitive. Not that $\N$ is transitive. To prove that $\N$ is transitive, one must apply the principle of mathematical induction to the set $\{x\in\N :x \subseteq \N\}$ and show that this set equals $\N$. This could perhaps be turned into another proof.

In response, I've edited the sentence "In other words, $\N$ is a transitive set." to "In other words, every element of $\N$ is a transitive set."


 * Thank you for that.
 * BTW please sign your posts on chat pages. --prime mover (talk) 05:21, 27 May 2013 (UTC)