Preimage vs Bijection - What's the difference?
preimage | bijection |
(mathematics) The set containing exactly every member of the domain of a function such that the member is mapped by the function onto an element of a given subset of the codomain of the function. Formally, of a subset B'' of the codomain ''Y'' under a function ƒ, the subset of the domain ''X defined by
(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 ,
As nouns the difference between preimage and bijection
is that preimage is (mathematics) the set containing exactly every member of the domain of a function such that the member is mapped by the function onto an element of a given subset of the codomain of the function formally, of a subset b'' of the codomain ''y'' under a function ƒ, the subset of the domain ''x defined by while bijection is (set theory) a one-to-one correspondence, a function which is both a surjection and an injection.preimage
English
(Function)Noun
(en noun)- For example, the preimage of {4, 9} under the squaring function is the set {?3,?2,+2,+3}.
Synonyms
* inverse imagebijection
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.