Well Ordering implies Induction Proof doubt
By construction, the smallest element of $S'$ has the form $k+1$ and so $k<k+1$ lies in $S$ as $\Bbb N_0 = S\cup S'$.
Well Ordering implies Induction Proof doubt
By construction, the smallest element of $S'$ has the form $k+1$ and so $k<k+1$ lies in $S$ as $\Bbb N_0 = S\cup S'$.