# Talk:Principle of Mathematical Induction

$\forall S\in\mathcal{P}(\omega)\,(\varnothing\in S \wedge \forall n\in S(n^+\in S) \Rightarrow S=\omega)$
is a consequence of $\omega$'s existence, its minimality property, and definition of set equality. I think its more immediate why the PMI applies to $\omega$ than to a Peano structure, as $\omega$'s existence has been demonstrated. Should we add this form? --Robertbiggs34 (talk) 21:16, 27 May 2013 (UTC)