what is the smallest unit of a real number to which it is composed of? I searched for relevant questions but my point is different. For example take set of real numbers with usual order then is the immediate successor of one. Firstly, I ask that is there any such number?? If yes then how surprisingly we beleive existence of a number but we cannot see that???

There is not such a number. Arguing by way of contradiction, for given $r\in\mathbb{R}$, suppose that $r_0$ is immediate successor of $r$. Then, $r<\frac{r+r_0}{2}< r_0$; a contradiction.
