A whole and its parts

     Aristotle may have been the first to assert that a whole is more than the sum of its parts.  Mathematics textbooks are likely to say otherwise, postulating that a whole is equal to the sum of its parts. 

     Emily Dickinson also comments on the matter.

                (1341)         by Emily Dickinson
 
     Unto the Whole -- how add?
     Has "All" a further realm --
     Or Utmost an Ulterior?
     Oh, Subsidy of Balm! 

Best words in the best order

     Writers of mathematics strive for clear and careful wording, especially in the formulation of definitions. Well-specified definitions can enable theorems to be proved succinctly. For example, the relation "less than" (denoted <) for the positive integers {1,2,3,...} may be defined as follows:

     If  a  and  b  are integers, then 
               a < b  if  b - a  is a positive integer. 

     Although the simple definition of "less than" as "to the left of" in the list {1,2,3,...} is intuitively clear, the formal definition above is better suited for mathematical arguments. It defines "less than" in terms of the known term, "positive." This sort of sequencing of definitions is common in mathematics -- one may go on to define "greater than" in terms of "less than," and so on.
     Saying things in the best way is also a goal of poetry. Well known to many are these words of poet Samuel Taylor Coleridge (1772–1834):