Domain and image of a function

[princessfrost]

We recall that Z is the set of all integers. For each i, j in Z, let f(i,j) be the larger of the two integers i and j. Do these remarks define a function? If so, what are the domain and the image?

I'm not sure how to do this. I believe that the remarks do define the function. But I don't know about the domain and image. Wouldn't the domain have to be bigger than the image making it Z^2 and the image Z?

Is this right?

Thanks for the help!

 

[Dick]

The domain is Z^2 and the image is Z. That's correct. But can you give better reasons?