Symbol for rational/irrational part of a number Just as $\Im(z)$ and  $\Re(z)$ denote the imaginary and real parts of $z$, respectively, do there exist symbols for the rational and irrational parts of a real number?

I think the closest thing you can get is the floor function. Where the "rational" or integer part of $x$ would be the largest integer less than or equal to $x$. But this doesn't really guarantee that what is left over will be irrational.

Edit
Thinking about it a bit more I think the following is at least well defined for real values of $x$,
$$ RationalPart(x) = \begin{cases} x \qquad x \in \mathbb{Q} \\ \lfloor x \rfloor \qquad x\notin \mathbb{Q} \end{cases} $$
Of course this doesn't have any of the nice properties like linearity that $Im$ and $Re$ have.
