> Floating point numbers give you that, problem solved. No. For example, floating point addition is not necessarily associative. In that sense, floating point

> Floating point numbers give you that, problem solved. No. For example, floating point addition is not necessarily associative. In that sense, floating point numbers aren't even a field and it's wrong to say that they can be used as a stand-in for real numbers. Floating-point numbers are incredibly useful and it is amazing that we can exactly analyze their error bounds, but it's wrong to treat them as if they were real numbers.