Meaning & Definition of word "Isomorphism"

Isomorphism

/ˌaɪsəˈmɔːrfɪzəm/

1. A mathematical or structural correspondence between two systems, where there is a one-to-one mapping that preserves relationships and properties.
- Example: The concept of isomorphism helps mathematicians understand the similarities between different algebraic structures.
2. In biology, a form of isomorphism may refer to two organisms that have similar form or structure but are genetically different.
- Example: The isomorphism observed between the bones of certain mammals illustrates adaptive evolution despite different lineages.
3. In computer science, isomorphism can refer to a mapping between two data structures that preserves their functional properties.
- Example: The programmer demonstrated an isomorphism between the two tree data structures, showing that they had identical traversal outcomes.
4. In category theory, it refers to a morphism that has an inverse, indicating a reversible transformation between objects.
- Example: 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.

Meaning: Equal structures

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

Meaning: Lookalikes

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