If $r$ is a machine-representable number and $f(r)$ is the next larger machine representable number, are the following true or false?
In fixed-point arithmetic, the distance between $r$ and $f(r)$ is constant.
In floating-point arithmetic, the relative distance $|(f(r)-r)/r|$ is constant.
I believe that (1) is true, but I'm not sure about (2). I am new to the world of numerical analysis and I'm just trying to hang on for dear life. Could anybody point me to a resource that does a good job of explaining the basic introductory topics of machine mathematics?