According to the definition in [Lang] p. 129: "A subset S of a module M is said to be <b>linearly independent</b> (over A) if whenever we have a linear combination ∑<sub>x∈S</sub>a<sub>x</sub>x which is equal to 0, then a<sub>x</sub> = 0 for all x ∈ S", and according to the Definition in [Lang] p. 130: "a familiy {x<sub>i</sub>}<sub>i∈I</sub> of elements of M is said to be <b>linearly independent</b> (over A) if whenever we have a linear combination ∑<sub>i∈I</sub>a<sub>i</sub>x<sub>i</sub> = 0, then a<sub>i</sub> = 0 for all i ∈ I." These definitions correspond to the definitions df-linds and df-lindf respectively, where it is claimed that a nonzero summand can be extracted (∑<sub>i∈{I\{j}}</sub>a<sub>i</sub>x<sub>i</sub> = -a<sub>j</sub>x<sub>j</sub>) and be represented as a linear combination of the remaining elements of the family.