Bijection vs Isomorphism - What's the difference?
bijection | isomorphism |
(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 ,
Similarity of form
* 1984 Brigitte Asbach-Schnitker, "Introduction", Mercury or The Secret and Swift Messenger , ISBN 9027232768.
(biology) the similarity in form of organisms of different ancestry
: (chemistry) the similarity in the crystal structures of similar chemical compounds
:* 1874 C. Rammelsberg,
: (sociology) the similarity in the structure or processes of different organizations
: 2. A one-to-one correspondence
: (group algebra) A bijection f'' such that both ''f'' and its inverse ''f −1 are homomorphisms, that is, structure-preserving mappings.
: (computer science) a one-to-one correspondence between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets
: (category theory) A morphism which has an inverse; the composition of the morphism and its inverse yields either one of two identity morphisms (depending on the order of composition).
As nouns the difference between bijection and isomorphism
is that bijection is a one-to-one correspondence, a function which is both a surjection and an injection while isomorphism is similarity of form.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.
Synonyms
* (function that is both a surjection and an injection) one-to-one correspondenceisomorphism
English
Noun
(en noun)- The postulated isomorphism between words and things constitutes the characterizing feature of all philosophically based universal languages.
"Crystallographic and chemical relations of the natural sulphides, arsenides, and sulpharsenides", The Chemical News and Journal of Physical Science , page 197.
- The isomorphism' of compounds does not prove the ' isomorphism of their respective constituents.