ISOMORPHISM Meaning and
Definition
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Isomorphism refers to a mathematical concept that describes a structural similarity or equivalence between two different systems or objects. Specifically, it involves the existence of a correspondence or mapping between elements of the first system/object and elements of the second system/object, such that certain properties or relationships are preserved.
In the field of mathematics, two particular structures are said to be isomorphic if there is a one-to-one correspondence between their elements that preserves the fundamental properties and operations of those structures. For example, in algebra, two groups are considered isomorphic if there exists a bijective homomorphism between them, meaning that the mapping preserves the group operations and the mapping is both injective (one-to-one) and surjective (onto).
Isomorphism can also be seen in other branches of mathematics, such as graph theory, where two graphs are isomorphic if there is a bijection between their vertices and edges that maintains adjacency relationships.
Furthermore, isomorphism can extend beyond mathematics into other fields like computer science and biology. In computer science, it is often used to describe the equivalence of two computational models or algorithms that perform the same tasks. In biology, isomorphism can refer to the similarity between the anatomical structures or forms of different organisms despite their evolutionary divergence.
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Similarity of form between two or more organisms or parts of the body.
A practical medical dictionary. By Stedman, Thomas Lathrop. Published 1920.
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The capability shown by two or more simple or compound substances to crystallise in one and the same form, or approximating very closely -and the similarity of form is generally combined with a similarity of other physical properties.
Etymological and pronouncing dictionary of the English language. By Stormonth, James, Phelp, P. H. Published 1874.
Common Misspellings for ISOMORPHISM
Etymology of ISOMORPHISM
The word "isomorphism" originated from the combination of two Greek words: "isos" meaning "equal" and "morphe" meaning "form" or "shape". The term was first introduced in the field of mathematics, specifically in the study of algebraic structures, to describe a special type of structure-preserving mapping between two entities that have the same structure, or "form". Over time, the concept of isomorphism has been adopted and applied in various other fields beyond mathematics.
Similar spelling words for ISOMORPHISM
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