Domain and image of a function

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SUMMARY

The discussion confirms that the function f(i,j), defined as the larger of two integers i and j from the set of all integers Z, is indeed a valid function. The domain of this function is Z^2, representing all ordered pairs of integers, while the image is Z, encompassing all integers. This conclusion is supported by the definition of a function, which requires a unique output for each input pair.

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

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