

-I L I B R A R Y 

 A LOGICAL NOTATION FOR MATHEMATICS-J^V ^•- 



By Robert T. A. Innes, F.R.A.S. 



Although my remarks apply to mathematics generally, the 

 'examples chosen will be confined to algebra, trigonometry and 

 the calculus. 



In algebra the learner is taught how to manipulate quantities 

 which are connected by various signs for addition, subtraction, 

 :multiplication and division and the brackets ; somewhat later he 

 is introduced to the indices and the radical for square and cube- 

 roots. When he fully understands that 



si means s ^ i 

 he has to learn that 



sin does not mean .s- x i x ii 

 and It is difficult to prove the logic in this distinction. 



I advocate (i) the use of the ordinary Roman lower case let- 

 ters, ordinary small type, italics and Clarendon type, and the 

 lower case Greek letters, and these only to be used for symbols of 

 quantity ; these furnish a hundred different symbols and they can 

 be manifolded by the use of suffixes as is so frequently done in 

 .astronomical formulae, but affixes should be barred as they are 

 apt to be confused with indicial numbers. 



(2) The capital letters of alphabets should be used purely and 

 simply as symbols of operation. An example is the operation of 

 "E on .V, viz. : 



x'- ,1:' 



E.i- = i+./:H 1 f-etc. 



2 1 "I 

 The rules suggested are, it is true, already partially in use. I 

 merely recommend that in mathematics, the most logical of the 

 sciences, thev should be rigidly and, therefore, logically adhered 

 to. Besides the gain in accuracy of form, the science will gain in 

 simplicity and the learner will not be troubled with some of the 

 absurdities which often cause real difficulties. It is known that 

 the beginning of the differential calculus is a stumbling block to 

 many ; this is at least partially caused by that most illogical 

 symbol of operation 



. which is not equal to . 



(^1/ 'J 



-as taught in algebra. 



The evolution of a satisfactory symbolical set of operators 

 will take some time, but there is no reason why some of the more 

 commonly used and simpler operators should not be introduced 

 forthwith ; especially do I appeal to writers of mathematical 

 books for teachers in South Africa to make a start, the more con- 

 fidently so as the translation from the logical system to the pre- 

 ■sent one is easily learned. If we refer to books on mathematics 

 -which are over two centuries old, we are apt to wonder at the 



