Definition
A set S is called countable if there exists an injective function f from S to the natural numbers
If f is also surjective and therefore bijective (since f is already defined to be injective), then S is called countably infinite.
As noted above, this terminology is not universal: Some authors use countable to mean what is here called "countably infinite," and to not include finite sets.
For alternative (equivalent) formulations of the definition in terms of a bijective function or a surjective function, see the section Formal definition and properties below.
Read more about this topic: Countable Set
Famous quotes containing the word definition:
“It is very hard to give a just definition of love. The most we can say of it is this: that in the soul, it is a desire to rule; in the spirit, it is a sympathy; and in the body, it is but a hidden and subtle desire to possess—after many mysteries—what one loves.”
—François, Duc De La Rochefoucauld (1613–1680)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)
“No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.”
—Florence Nightingale (1820–1910)