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I need to prove (or disprove) that the sum of surjective funcitons is surjective.

However, I keep getting stuck up on one thing. If f(x) has the codomain Y and g(x) has the codomain Z, does (f+g)(x) have the codomain Y + Z (or Y U Z)? I can very easily state for this proof that for all y (and for all z) that there exists an x where f(x) = y (and that there exists an x where g(x)=z.)

I don't know how to follow this proof through to the sum function though. SOrry I'm not good at this theory/proof stuff.