If 
is a map
(a.k.a. function, transformation,
etc.) over a domain 
, then the range of 
, also called the image of 
under 
,
is defined as the set of all values that 
can take as its argument varies over 
, i.e.,
 |
Note that among mathematicians, the word "image" is used more commonly than "range."
The range is a subset of 
and does not have to be all of 
.
Unfortunately, term "range" is often used to mean domain--its precise opposite--in probability theory, with Feller (1968, p. 200) and
Evans et al. (2000, p. 5) calling the set of values that a variate 
can assume (i.e., the set of values
that a probability
density function 
is defined over) the "range", denoted by 
(Evans et al. 2000, p. 5).
Even worse, statistics most commonly uses "range" to refer to the completely different statistical quantity as the difference between the largest and smallest order statistics. In this work, this form of range is referred to as "statistical range."
