I sometimes hear people saying something like
Let $f$ be a function from a set $A$ into another set $B$.
But, of course, by saying this, they do not want to exclude the possibility of $A$ and $B$ being equal, they just mean that $B$ can be different than $A$.
My question is: Is it, technically speaking, correct to use the word "another" in this case? Also, independent of the question whether "another" is correct or not, I wonder if the word "another" could confuse readers oder listeners, that is, if the word "another" is good from an expository point of view.