Concept

Enumeration

Overview

An enumeration is a complete, ordered listing of all the items in a collection. The term is commonly used in mathematics and computer science to refer to a listing of all of the elements of a set. The precise requirements for an enumeration (for example, whether the set must be finite, or whether the list is allowed to contain repetitions) depend on the discipline of study and the context of a given problem.

Some sets can be enumerated by means of a natural ordering (such as 1, 2, 3, 4, ... for the set of positive integers), but in other cases it may be necessary to impose a (perhaps arbitrary) ordering. In some contexts, such as enumerative combinatorics, the term enumeration is used more in the sense of counting – with emphasis on determination of the number of elements that a set contains, rather than the production of an explicit listing of those elements.

Overview adapted from Wikipedia (CC BY-SA 4.0; see the article history for authors).

In the original texts

Passages from public-domain books where Enumeration is discussed.

But you did not buy it, nor did it come to you by inheritance, nor was it foaled on your estate, nor was it given to you as a present, therefore you must certainly have stolen it." This enumeration is fairly reprehended, if it can be alleged that the horse was taken from the enemy, as that description of booty is not sold. And if that be alleged, the enumeration is disproved, since that matter has been stated which…
Marcus Tullius Cicero, The Orations of Marcus Tullius Cicero, Volume 4
names the idea; states what it is
Read the chapter · Open in the reader
And in the case of an infinite class, enumeration is impossible, so that description by a general characteristic common and peculiar to the members of the class is the only possible description. Here, as we see, the theory of number to which Frege was led by purely logical considerations becomes of use in showing how infinite classes can be amenable to number in spite of being incapable of enumeration.
Bertrand Russell, Our Knowledge of the External World as a Field for Scientific Method in Philosophy
states what it is; names the idea
Read the chapter · Open in the reader
But we are not entitled to assume this in the commencement. We must begin by recognising the distinctions made by ordinary language. If some of these appear, on a close examination, not to be fundamental, the enumeration of the different kinds of realities may be abridged accordingly. But to impose upon the facts in the first instance the yoke of a theory, while the grounds of the theory are reserved for discussion…
John Stuart Mill, A System of Logic
names the idea; opens on it
Read the chapter · Open in the reader
We have suffered much from critics who consider it sufficient to criticise our procedure on the slender basis of a knowledge of the dictionary meanings of such terms. For example, a one-to-one correlation depends on the notion of a class with only one member, and this notion is defined without appeal to the concept of the number one. The notion of diversity is all that is wanted.
Alfred North Whitehead, The organisation of thought, educational and scientific
states what it is; opens on it; names the idea
Read the chapter · Open in the reader
The necessity of an enumeration of Existences, as the basis of Logic, did not escape the attention of the schoolmen, and of their master Aristotle, the most comprehensive, if not also the most sagacious, of the ancient philosophers. The Categories, or Predicaments—the former a Greek word, the latter its literal translation in the Latin language—were believed to be an enumeration of all things capable of being named…
John Stuart Mill, A System of Logic, Ratiocinative and Inductive
names the idea; opens on it
Read the chapter · Open in the reader

Related ideas

Place in the tradition

Part of Outline of logic.

Explore Enumeration in the interactive graph →