Isomorphism

/ˌaɪsəˈmɔːrfɪzəm/

Meaning & Definition

noun

A mathematical or structural correspondence between two systems, where there is a one-to-one mapping that preserves relationships and properties.

The concept of isomorphism helps mathematicians understand the similarities between different algebraic structures.

In biology, a form of isomorphism may refer to two organisms that have similar form or structure but are genetically different.

The isomorphism observed between the bones of certain mammals illustrates adaptive evolution despite different lineages.

In computer science, isomorphism can refer to a mapping between two data structures that preserves their functional properties.

The programmer demonstrated an isomorphism between the two tree data structures, showing that they had identical traversal outcomes.

In category theory, it refers to a morphism that has an inverse, indicating a reversible transformation between objects.

In the category of sets, every bijection is an isomorphism, demonstrating a perfect correspondence between the two sets.

From the Greek 'iso-' meaning 'equal' and 'morphe' meaning 'form.'

isomorphic structures

Structures that exhibit an isomorphic relationship.

isomorphic mapping

The process of creating an isomorphism between two mathematical entities.

group isomorphism

A specific type of isomorphism where two groups are identical in structure.

isomorphic

Adjective describing entities that share an isomorphic relationship.

isomorph

An entity that is isomorphic to another.

Equal structures

In math, we often say two groups are isomorphic if they're just equal structures.

Lookalikes

Those two functions are isomorphs; they’re basically lookalikes in function space.