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... you must know my attitude to you. I do not know you as a man completely but I guess a warm and admirable personality. However, one thing I know for certain: the range of your mental powers which, so far as I accustomed myself to guess people, open up limitless possibilities in science. I will not utter the appropriate word—what for? Talent—this would belittle you. You are entitled to get more... In 1935 Kantorovich made his major mathematical discovery—he defined K-spaces, i. e., vector lattices whose every nonempty order bounded subset had an infimum and supremum. The Kantorovich spaces have provided the natural framework for developing the theory of linear inequalities which was a practically uncharted area of research those days. The concept of inequality is obviously relevant to approximate calculations where we are always interested in various estimates of the accuracy of results. Another challenging source of interest in linear inequalities was the stock of problems of economics. The language of partial comparison is rather natural in dealing with what is reasonable and optimal in human behavior when means and opportunities are scarce. Finally, the concept of linear inequality is inseparable from the key idea of a convex set. implies the existence of nontrivial continuous linea