6 pitcher: interrelations of 



- or 



— not 



[ ] a class of (elements; functions; etc.) 

 [all ] the class consisting of all (elements; functions; etc.; having 



a specified property or satisfying a specified condition) 

 U l'^] the least common superclass of the classes ^1.^ of the class 



[^] of classes 

 n ['^] the greatest common subclass of the classes ^ of the class 



C^^] of classes 



2. The General Analysis of Moore is concerned with the theory of 

 real-valued, single-valued functions on a general variable. Otherwise 

 stated it is concerned with functions on 'ip to 51 where '$ = [p] is a 

 general class of elements* and 31 = [a] is the class of all real numbers. A 

 function assigns to each element p a real number a. 



Moore adopts the terminology of the theory of functions, f Denote 

 a function on ^13 to 21 by p. Then p is the variable of the function p; 

 the class '^ is the range (of the variable) of the function fx; at the 

 argument value or place p the function /x has the functional value ixp, 

 etc. 



Such a function n is indicated by the various notations : 



M, (Mp), (MpIp), (MpIp*)- 



The last notation may be read: " The system of (functional) values y.p 

 where p varies over the class "ip." The intention is to discriminate 

 sharply between function and functional value. 



The general theory relates to properties of classes 2)? of systems 

 (21; "iP; W) where 21 and '^ are defined as above and 



m ^ [m] 



is a class of functions on '^ to 21. 



In particular the following special systemsf are noticed: 

 (I) ^V is the class of a single element: e. g., p = 1. 



SJJ' is the class of all functions on ^^ to 21, i. e., in effect 9)J' is the 

 real number system 21. 

 (II„) ^"" is the class of n elements: e. g., "ip = 1, 2, ■ • ■ n. 



* German capitals are used to denote classes. The elements of these classes are denoted 

 by the corresponding small Greek or Latin letters. 



1 1. G. A., § 4. Moore here indicates a more general function F on ^^ to 1*'. 

 tl. G. A., §5. 



