The terminology is the other way round. The range (also called the image) of a function is the set of values it actually takes. The codomain is whichever superset of the range you are considering as the set the function maps to, the “result type” of the function. So the range of the +1 function on the domain ℕ is the positive integers, but the codomain is any superset of that, and gives a different morphism in the category Set for each one.
Whelp, I’ve been getting that wrong for some time now, thanks.
Ah, apparently “range” is ambiguously used as both “codomain” and “image”. I think I was taught it as codomain (before I was taught that word), and then at some point started to think of codomain as “the one that isn’t the range”.
The terminology is the other way round. The range (also called the image) of a function is the set of values it actually takes. The codomain is whichever superset of the range you are considering as the set the function maps to, the “result type” of the function. So the range of the +1 function on the domain ℕ is the positive integers, but the codomain is any superset of that, and gives a different morphism in the category Set for each one.
Whelp, I’ve been getting that wrong for some time now, thanks.
Ah, apparently “range” is ambiguously used as both “codomain” and “image”. I think I was taught it as codomain (before I was taught that word), and then at some point started to think of codomain as “the one that isn’t the range”.
https://en.wikipedia.org/wiki/Range_(mathematics)
It’s older terminology. Everyone says image now.
I thought I had it right, and then mixed it up in my head myself.