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"). An ordered pair where the first coordinate is formula_1 and the second coordinate is formula_2 is usually written formula_3 (sometimes it is written formula_4). If formula_1 is different from formula_2, then the ordered pair formula_3 is different from the ordered pair formula_8 - this is why it is called "ordered".