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You already said it all: the only constraint to have a function is that the x-values must be distinct for distinct y-values. There is no other restriction. (It happens that here all values are integers, but that's not part of the definition of a function.) But it could a priori happen that a given pair (x,y) is listed twice.
Functions or Not?
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You already said it all: the only constraint to have a function is that the x-values must be distinct for distinct y-values. There is no other restriction. (It happens that here all values are integers, but that's not part of the definition of a function.) But it could a priori happen that a given pair (x,y) is listed twice.