Math Challenges

Solution:
\( \left\lbrace0\right\rbrace\cup\left\lbrace\frac{1}{n}:n\in\mathbb{N}\right\rbrace\cup\left\lbrace1\right\rbrace\cup\left\lbrace1+\frac{1}{n}:n\in\mathbb{N}\right\rbrace\cup\left\lbrace2\right\rbrace\cup\left\lbrace2+\frac{1}{n}:n\in\mathbb{N}\right\rbrace \)