What to choose for co-domain, somewhat confused

[jaejoon89]

When you choose the co-domain can it just be anything that is greater than the range (i.e. the image)? In general, should the co-domain just be whatever space it maps to: R^2, R^3, etc. whereas the range is a subset of that space such as R^+ (all positive reals)?

 

[VeeEight]

Yes, the codomain is the space that the function maps to - that is, all the possible outcomes. This is usually given in the definition of the function. The image/range is what actually comes out. The wikipedia page for http://en.wikipedia.org/wiki/Codomain" has some examples