"A Treatise on Universal Algebra " sought to examine Hermann Grassmann's theory of extension ( " Ausdehnungslehre " ), Boole's algebra of logic, and Hamilton's quaternions ( this last number system was to be taken up in Volume II, which was never finished due to Whitehead's work on " Principia Mathematica " ).
12.
In a review Alexander Macfarlane wrote : " The main idea of the work is not unification of the several methods, nor generalization of ordinary algebra so as to include them, but rather the comparative study of their several structures . " At the time George Boole's algebra of logic made a strong counterpoint to ordinary number algebra, so the term " universal " served to calm strained sensibilities.
13.
Ernst Schr�der in " The Algebra of Logic " consolidated and advanced the work of Boole and Peirce introducing the concept of the reflexive relation, and Alfred Tarski, adhering to Schr�der s notation, introduced further types of relation in his paper " On the Calculus of Relations " published in 1941 where he said We may for instance distinguish certain important categories of relation such as symmetric relations, transitive relations, ordering relations, one-many relations & and one-one relations & .
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