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MATHEMATICS: E. H. MOORE 
of normal sculpture. As far as I have seen and read, the range is unique 
in this systematic tripartite arrangement of normally and glacially sculp- 
tured forms. A fuller account of the range will be prepared for the 
Bulletin of the American Geographical Society. 
DEFINITION OF LIMIT IN GENERAL INTEGRAL ANALYSIS 
By Eliakim Hastings Moore 
DEPARTMENT OF MATHEMATICS. UNIVERSITY OF CHICAGO 
Presented to the Academy. November 8, 1915 
L General Analysis. The problem of Science is the organization of 
and the study of the interrelations amongst the objects and phenomena 
of Nature. Analogous objects or phenomena are grouped into classes. 
In the progress of Science, with the discovery of new objects or phenom- 
ena or interrelations, the bases of classification initially of necessity 
superficial become more fundamental; thus in Physics, Electricity and 
Magnetism and later Light merge in Electromagnetism. 
Mathematics with its source in Nature progresses in similar fashion. 
Hence, remembering that the objects or phenomena of Mathematics 
may be theories (doctrines), we may enunciate the following heuristic 
principle : 
The existence of analogies between central features of various theories 
implies the existence of a more fundamental general theory embracing the 
special theories as particular instances and unifying them as to those 
central features. 
After the development of such a general theory, the fact that the 
various theories are instances of the general theory implies as an obvious 
consequence (and accordingly eclipses in importance) the analogies 
between the central features of the various theories. In illustration of 
the heuristic principle may be adduced the theories of General Analysis 
mentioned below. 
Analysis is the branch of Mathematics devoted to the classification 
of and the study of the interrelations amongst numerically valued 
functions. A (single- valued) function r or r(^) is a table (or rule or 
process) assigning to every element or member ^ of a certain class or 
range *ip a definite element ^ of a certain class O. It is numerically 
valued in case the functional values q, = t{p), are numbers real or 
complex. Although not always numerical, the independent variable 
^ of a function r considered in a theory of Classical Analysis is always 
of specified nature; e.g., the variable p may be a curve or a numerically 
