Explicitly, the first Chern class can be defined as follows. For a line bundle "L" on an integral Noetherian scheme "X", let "s" be a nonzero rational section of "L" (that is, a section on some nonempty open subset of "L"), which exists by local triviality of "L". Define the Weil divisor ("s") on "X" by analogy with the divisor of a rational function. Then the first Chern class of "L" can be defined to be the divisor ("s"). Changing the rational section "s" changes this divisor by linear equivalence, since ("fs") = ("f") + ("s") for a nonzero rational function "f" and a nonzero rational section "s" of "L". So the element "c"1("L") in Cl("X") is well-defined.