CHANGE 2/6 



2/6. Notation. Many transformations become inconveniently 

 lengthy if written out in extenso. Already, in S.2/3, we have been 

 forced to use dots ... to represent operands ihat were not given 

 individually. For merely practical reasons we shall have to develop 

 a more compact method for writing down our transformations, 

 though it is to be understood that, whatever abbreviation is used, 

 the transformation is basically specified as in S.2/3. Several 

 abbreviations will now be described. It is to be understood that 

 they are a mere shorthand, and that they imply nothing more than 

 has already been stated expHcitly in the last few sections. 



Often the specification of a transformation is made simple by 

 some simple relation that links all the operands to their respective 

 transforms. Thus the transformation of Ex. 2/4/1 can be replaced by 

 the single line 



Operand — > operand plus three. 



The whole transformation can thus be specified by the general rule, 

 written more compactly, 



Op.-^Op. + 3, 



together with a statement that the operands are the numbers 1, 2, 

 3 and 4. And commonly the representation can be made even 

 briefer, the two letters being reduced to one: 



«^rt + 3 (« = 1,2, 3, 4) 



The word "operand" above, or the letter n (which means exactly 

 the same thing), may seem somewhat ambiguous. If we are thinking 

 of how, say, 2 is transformed, then "«" means the number 2 and 

 nothing else, and the expression tells us that it will change to 5. The 

 same expression, however, can also be used with n not given any 

 particular value. It then represents the whole transformation. It 

 will be found that this ambiguity leads to no confusion in practice, 

 for the context will always indicate which meaning is intended. 



Ex. 1 : Condense into one line the transformation 



I 1 2 3 

 ^ II 12 13 



E.X. 2 : Condense similarly the transformations : 



rl-> 7 fl-^l f'-^l 



a:<^2-^14 b:<^2->4 c:<^2-^l/2 



13-^21 l3^9 l3^1/3 



■i->io fi-^i r^-^1 



2-^9 e: ^ 2->l f: ■{ 2 -> 2 



.3-^ 8 l3->l l3->3 



13 



