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:
“I’m beginning to think that the proper definition of “Man” is “an animal that writes letters.””
—Lewis Carroll [Charles Lutwidge Dodgson] (1832–1898)
“... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
—George Eliot [Mary Ann (or Marian)
“... if, as women, we accept a philosophy of history that asserts that women are by definition assimilated into the male universal, that we can understand our past through a male lens—if we are unaware that women even have a history—we live our lives similarly unanchored, drifting in response to a veering wind of myth and bias.”
—Adrienne Rich (b. 1929)