The Grammar According to West

Summary

The first section of the paper is an "Introduction" that should motivate the problem, discuss related results, state the results more completely, and perhaps summarize the techniques or the structure of the paper or crucial definitions. Definitions. Words being defined should be distinguished by italics (or perhaps boldface in a textbook context). When italics are used to indicate a word being defined, it is unnecessary to use "called" or "said to be"; the use of italics announces that this is the term being defined and replaces these words. Many definitions are phrased as "An object has property italicized term if condition holds." Here we use the word "if" even though subsequently it is understood that an object satisfies the property being defined if and only if the given condition holds. The italicization alerts the reader to this situation. The convention can be justified by saying that the property or object does not actually exist until the definition is complete, so one does not yet in the definition formally say that the named property is equivalent to the condition. Definitions written by non-native speakers sometimes contain extra commas. In each sentence below, the comma should be deleted. "A bipartite graph, is a graph that is 2-colorable". "A graph is bipartite, if it is 2-colorable". The first example is a mistaken placement of a comma inside a clause (see discussion of Commas). Note the difference in italicization above. When written as an adjective-noun combination, the term being defined is the name for structures that have the property; hence the full term bipartite graph is italicized. When the property alone is being defined and is positioned as a predicate adjective, only the adjective is italicized. Double-Duty Definitions. One cannot make a statement about an object before the object has been defined. Similarly, one cannot use notation as part of a formula making a statement about the denoted object unless the notation has previously been def...