How to show that for any $n\in\Bbb N\;,n^+=n+1$

Question

Show that for Any $n\in\Bbb N\;,n^+=n+1$

We know for $ n=0 , 0^+=1+0$ for $n\in\Bbb N$ supposing that $n^+=1+n$ then have to show $(n+1)^+=n+1+1=n^++1$

Answer 1

$(n+1)^{+} = (n^{+})^{+} = n^{+} + 1 = (n+1) + 1$