About the particularities of infinite systems

Based on previous results on the study of infinite systems studied basic common fundamental differences of general infinite systems from finite. In particular, it is shown that are not fulfilled Fredholm and Noether's theorems to the general infinite system of linear algebraic equations. In addition, to clarify the concept of the reduction method. In particular, we show that it can converge, but not to the solution considered infinite system. It is also pointed out that the reduction method for solution of homogeneous infinite systems exhibits duality. It is noted that the solution of homogeneous infinite systems is controversial in relation to the solution of finite homogeneous systems. In particular, it is shown that an infinite homogeneous system may have non-trivial solutions, even though its infinite determinant is not zero. In addition, the solution of the linear homogeneous infinite system is necessarily reduced to the solution of the nonlinear equation, the so-called characteristic equation, which is impossible for finite systems.