The question of the existence of a committee of a system of linear inequalities under additional conditions is considered. The most part of the article is devoted to the results of the research conducted by Vl.D. Mazurov and M.Y. Khachai on the committees of systems of linear inequalities. The given article represents the continuation of the results. The question of the proofs of the results in infinite-dimensional case is answered. This is the most difficult part of the problem. The committee of a system of algebraic inequalities is an ordered set of decision rules on the basis of which the final procedure of decision making is formed. The problem of committee construction and their application in economics and technics is topical since their initial formulation often contains controversies and non-formalized parts. Therein the system of homogeneous linear inequalities with an infinite set of indices is considered. Solution set can be empty as well. The conditions are proved under which there exist a committee of the system. As it follows from the theorem when the number of limit points in the left parts of inequalities is finite then the problem is reduced to that of construction of mutually independent committees. The example is given. At present factor analysis with the similar features is becoming increasingly important, the given mathematical apparatus can be applied to them as well. Further on, these methods are applied in psychology including a depth one the research of which was initiated by Carl Jung.