Laws of motion

above is Newton's second law 

But it should be conditional beacuse 

we can write it as  a =F/m. and  a is relative quantity and f / m is absolute quantity and hence we can predict that Newton's second law is  conditional  but it is not wrong.  

Condition to Newton's second law is inertial frame because Newton choose this only because of simplicity in calculate force

Definition of inertial frame was given by Newton in his first law .Second law is only useful in inertial frame and definition of inertial frame is given by Newton in his first law 

Newton's first law is

This law is given by Newton and by your textbooks. But I says that Newton's first law's this version doesn't helpful to explain the condition to Newton's second law then it has modified by top physicists and then Newton's first law becomes

" A body which acted by net force zero seen by a frame which predicts acceleration of the body is zero that frame is inertial frame " 

Golden statement: Newton's first law only says the definition of inertial frame nor the special case of second law