Modeling a greatest integer function I'm trying to model a function that resembles a greatest integer function. The domain is from [0, $\infty$). The inputs from 0 to 1.5 (non-inclusive) need to be mapped to an output of 0, and 1.5 to $\infty$ mapped to 1. But, I'm trying to not use a piecewise function. Is it possible to accomplish this?
Here's what I've tried:
$$f(x)=\left\lfloor \frac{x}{1.5} \right\rfloor$$

Try this function,
$$\frac{|x-1.5|}{2x-3}+\frac12$$
Although this is very artificial, it works.
