A collection is certainly a more basic notion than a combination as is demonstrated by the fact that a combination is defined as a collection of a specific kind I tend to agree that the word objects looks redundant in the present formulation so would it be better if we wrote In mathematics an ordered pair is a collection of objects having two coordinates or entries or projections such that it is distinguishable which object is the first coordinate or first entry or left projection of the pair and which object is the second coordinate or second entry or right projection of the pair Would that be an improvement Re how do you tell which coordinate is which it is easy the first coordinate is the which happens to be the second coordinate as well in this specific case