Question Number 147800 by 0731619 last updated on 23/Jul/21
Answered by Olaf_Thorendsen last updated on 23/Jul/21
$$\mathbb{R}\:=\:\underset{{n}\in\mathbb{Z}} {\cup}\mathrm{E}_{{n}} ,\:\mathrm{E}_{{n}} \:=\:\left[{n},{n}+\mathrm{1}\left[\right.\right. \\ $$$$\forall{x}\in\mathrm{E}_{{n}} ,\:\left\{{x}\right\}\:=\:{x}−\lfloor{x}\rfloor\:=\:{x}−{n} \\ $$$$\forall{x}\in\mathrm{E}_{{n}} ,\:\frac{{d}}{{dx}}\left\{{x}\right\}\:=\:\mathrm{1} \\ $$