exact and approximate

In 2.5.1.4 you are defining approximate datatypes as follows:

Then for every value v' in C, there is a corresponding value v in M and a real
value h such that P(x) = v' for all X in M such that |v - x| < h.

First of all, because of absolute value,  h should be >0 (or >=0).
Then x in M must  be different from v in M. So, you better say , for example,
... and a real value h >0 such that P(x) = v' for all x != v in M such that |v -
 x| < h

Next:  Furthermore, for at least one value v' in C, there is more than one value
 y in M such that P(y) = v'
Question: is it possible for  v'' from C and v'' !=v' that P(y) =v' and
P(y)=v''?
 I am just trying to understand your concept of "approximate datatype".

Thanks