In mathematics , an ordered pair is a collection of two objects , where one of the objects is first ( the first coordinate or left projection ) , and the other is second ( the second coordinate or right projection ) . 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 .