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DEFINITION of 'Boolean Algebra'. A division of mathematics which deals with operations on logical values. Boolean algebra traces its origins to an 1854 book by mathematician George Boole. The distinguishing factor of Boolean algebra is that it deals only with the study of binary variables. Most commonly boolean variables are presented with the possible values of 1 (true) or 0 (false).
foundations of mathematics. ...1, where 0 is the empty set and 1 is the set consisting of 0 alone. Both definitions require an extralogical axiom to make them workâthe axiom of infinity, which postulates the existence of an infinite set. Since the simplest infinite set is the set of natural numbers, one cannot really say that arithmetic has been reduced to logic.