MIN_VALUE tells you how precise a float can get, but not the mathematical minimum it can represent. They should have named it better...
Negative of MAX_VALUE is the mathematical minimum value for floats(same goes for double).
The reason you can assume this has to do with how numbers are represented in binary:
Java float and doubles use sign bit to represent negative/positive values as opposed to two's complement representation for integers. This means it's positive and negative value have the same magnitude, ie. -(positive max) = negative max. Therefore you don't need to define an actual mathematical minimum constant for floats because you can just use the positive max constant to figure out the what the negative bound is. For integers, you need 2 different constants defining max/min because of the way they represented in binary, i.e. -max != min.
For more info http://people.uncw.edu/tompkinsj/133/numbers/Reals.htm
