$\mathbb N_k$ = { n $\in$ $\mathbb N$: n $\le$ k}, let k $\ge$ 2. Define r: $\mathbb N_k$ $\to $ $\mathbb N_k$ by r(k)=1 and for all x $\in$ $\mathbb N_k$ , if x < k, then r(x)=x+1. Prove r is one-to-one and onto.
I'm sorry if this looks weird. This is my first time posting here and I couldn't find a guide on how to properly post mathematical symbols, etc.
I don't really know where to even begin proving this. Upon looking at it, all I can tell is that it doesn't appear to be one-to-one, but I'm not sure about onto. I don't have a complete understanding of that term.
Any help would be appreciated, thanks!
Note: 0 $\notin$ $\mathbb N$