The use of \mathbb{R} for floats acts to obscure things for me I'm afraid. It loads up dusty old stuff in my brain about the reals that is not true of floats from the slow tape archive storage in my skull, and _doesn't_ load up stuff in my brain about floats like, say, where the first integer gap occurs[1]. A side note is that \mathbb{Q} would be a closer match to float.

[1] http://stackoverflow.com/questions/3793838/which-is-the-firs...