What does {$x$} mean?

Question

What does {$x$} mean in terms of $x$? I'm not really sure about anything on this so please explain as thoroughly as possible. Thanks!

Answer 1

As a hint:
$$\forall x \in \mathbb{R} :x=\lfloor x \rfloor +\{x\} $$for example $$x=3.53 \to \lfloor x \rfloor=3 , \{x\}=0.53\\x=4\to \lfloor x \rfloor=4 , \{x\}=0 \\x=-3.7 \to \lfloor x \rfloor=-4 , \{x\}=+0.3$$ also you can rewrite $\{x\}=x- \lfloor x \rfloor$ for the last example $$x=-3.7 \to \lfloor x \rfloor=-4 \\\{x\}=x-\lfloor x \rfloor=-3.7-(-4)=+0.3$$ and finally $$0\le \{x\} <1$$