Is the codomain and range of an onto function the same? As far as I understand, if $f:A\to B$, range is all possible values in B. So if it's an onto function, then all values in B must be mapped to something in A right? Am I correct?

up vote 4 down vote accepted

Is the codomain and range of an onto function the same?

Yes, by definition a function $f:A\to B$ is onto if the range ($f(A)$) equals the codomain ($B$).

So if it's an onto function, then all values in B must be mapped to something in A right? Am I correct?

I'm not sure you wrote what you meant to write. All values in $B$ must be mapped to by something in $A$, yes.

  • thanks! sorry I didn't know onto functions were defined like that. I was taught only the definition that a function is onto if " All values in B must be mapped to by something in A" – Teerex Nov 8 at 20:44
  • @Teerex ... but those two things are semantically identical. You were taught that definition. They are the same, just with different notation. It's worth thinking about a little. – rschwieb Nov 8 at 20:57

Your Answer

 

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.