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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?

nonuser
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Anna
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1 Answers1

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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.

rschwieb
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  • 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" – Anna Nov 08 '18 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 08 '18 at 20:57