Another question was, Let S be a finite set $\displaystyle \{z_1, z_2, z_3,\cdots z_n\}$ where z=a+bi. Prove S is bounded.

For this one, I said since S is finite, S is can be put in a 1-1 correspondence with $\displaystyle \mathbb{N}$.

Also, I was allowed to assume $\displaystyle S\subset\mathbb{C}$.

I then said $\displaystyle S\subseteq\mathbb{N}$.

Now, we have $\displaystyle S\subseteq\mathbb{N}\subset\mathbb{C}$.

So S must be bounded. I know it is wrong but how should it be done or what could I have added or altered to make it correct?