Hello!

Please help me prove the following,

Let $\displaystyle n\in\mathbb{N}$. Show that there exist infinite $\displaystyle B\subseteq\mathbb{N}-\{n \}$ such that $\displaystyle f$ is constant on all sets of the form $\displaystyle \{n,b\}$ where $\displaystyle b\in B$.

Thank you!