Bijection vs Countable - What's the difference?
bijection | countable |
(set theory) A one-to-one correspondence, a function which is both a surjection and an injection.
* 2002 , Yves Nievergelt, Foundations of Logic and Mathematics ,
* 2007 , C. J. Date, Logic and Databases: The Roots of Relational Theory ,
* 2013 , William F. Basener, Topology and Its Applications ,
Capable of being counted; having a quantity.
(mathematics, of a set) Countably infinite; having a bijection with the natural numbers.
(mathematics, of a set) Countably infinite or finite; having a bijection with a subset of the natural numbers.
(grammar, of a noun) Freely usable with the indefinite article and with numbers, and therefore having a plural form.
As a noun bijection
is (set theory) a function which is both a surjection and an injection.As a adjective countable is
capable of being counted; having a quantity or a numerical attribute.bijection
English
(wikipedia bijection)Noun
(en noun)page 214,
- The present text has defined a set to be finite if and only if there exists a bijection' onto a natural number, and infinite if and only if there does not exist any such ' bijection .
page 167,
- Note in particular that a function is a bijection if and only if it's both an injection and a surjection.
unnumbered page,
- The basic idea is that two sets A and B have the same cardinality' if there is a '''bijection''' from A to B. Since the domain and range of the '''bijection''' is not relevant here, we often refer to a '''bijection''' from A to B as a '''bijection between the sets''', or a ' one-to-one correspondence between the elements of the sets.