Abstract

This chapter discusses the elements of mathematical logic. Mathematical logic developed as a result of the application of mathematical methods to the problems of formal logic and as a discipline serving the ends of the foundations of mathematics. Mathematical logic has received diverse technical applications. Contemporary mathematical logic is connected with automation, with machine mathematics and problems of automatic translation from one language to another, with information theory, and with cybernetics. The methods of mathematical logic find wide applications in the theory of electrical networks with switching action. In algebra, numbers—the objects of the study of arithmetic—are denoted by letters. The object of that part of mathematical logic that is known as the propositional calculus is the study of propositions. The propositional calculus is the most elementary part of mathematical logic. Mathematical logic distinguishes carefully between the different ways of using variables and fixes them with the aid of a special symbolism.

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