How should the following statement be interpreted: Let $f$ be a function with range in* $[0,1]$. (Here the word "in" has been deliberately included.)
In this context, the range is the same as the image.
I've always taken the statement to mean that the image of $f$ lies in $[0,1]$. Are there alternate interpretations of this statement? For example, can the above statement also mean that the image of $f$ is exactly $[0,1]$?