Inserting back slash between left and right braces

Question

I want to write (Natural number set) \ (singleton $n$). How do I write this? The code is

\documentclass[12pt,a4paper]{article}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\begin{document}
    \mathbb{N}\\{n\}
\end{document

But \mathbb{N}\\{n\} does not seem to work.