countable and uncountable sets::
If this f is also surjective and therefore bijective, then S is called countably infinite.
In other words, a set is called "countably infinite" if it has one-to-one correspondence with the natural number set, N.
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
Definition of countable::
A set S is called countable if there exists an injective function f from S to the natural numbers N = {0, 1, 2, 3, ...}.[4]If this f is also surjective and therefore bijective, then S is called countably infinite.
In other words, a set is called "countably infinite" if it has one-to-one correspondence with the natural number set, N.
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
No comments:
Post a Comment