"Isomorphism" Pronounce,Meaning And Examples
"Isomorphism" Natural Recordings by Native Speakers
"Isomorphism" Meaning
In mathematics, an isomorphism is a bijective homomorphism between two algebraic structures, such as groups, rings, or vector spaces. In other words, it is a function between the structures that is both one-to-one (injective) and onto (surjective), and preserves the algebraic operations. Isomorphism is often used as a theoretical tool to prove that two structures are essentially the same, even if they have different underlying sets or operations.
"Isomorphism" Examples
Isomorphism
A mathematical concept used in group theory and abstract algebra that describes two algebraic structures having the same underlying set and similar operations.
Examples:
The real numbers under addition and the integers under addition are isomorphic, as one can be explicitly mapped to the other by adding 1 to each integer, thus showing that they have the same structure.
The quadratic formula x (-b ± √(b^2 - 4ac)) / 2a reveals an isomorphism between the quadratic expressions and the complex numbers.
In computer science, isomorphism can be seen in the relationship between abstract syntax trees (ASTs) of two programs written in the same programming language, despite the programs having different source code.
In linguistics, the relationship between two languages with identical grammatical structures but different vocabulary can be considered an isomorphism.
In biology, the concept of isomorphism can be applied to the study of developmental biology, where two organisms may have the same developmental processes and pathways despite having different DNA sequences.
"Isomorphism" Similar Words
Isometrically
Isometrically refers to the relationship between shapes, figures, or objects that have the same size and shape when viewed from different angles or perspectives, meaning that their dimensions and proportions are the same when seen from different sides or directions.
Isometrics
Isometries
Isometropia
Isometropia is a medical term that refers to a specific type of refractive error in which the eyeball is perfectly spherical, meaning that the distance from the center of the eye to the cornea is equal to the radius of the eye. This is considered a normal or ideal shape, and isometropia is often used as a reference point for comparison with other types of refractive errors. In other words, if someone has isometropia, their eyeball is perfectly shaped, meaning that the distance from the front of the cornea to the back of the eye (the posterior pole) is equal to the radius of the eye.
Isometry
Isomonic
Isomorph
Isomorph refers to something that has the same shape or structure as something else, but is not necessarily identical. It can also refer to a molecule or crystal that has the same external shape as another molecule or crystal, but has a different internal composition. In mathematics, isomorphs are objects that are identical in structure or form, but may have different values or properties.
Isomorphic
Isomorphisms
Isomorphisms is a mathematical term that refers to a bijective homomorphism, which is a function between two algebraic structures, such as groups, rings, or fields, that preserves their operations and properties. In other words, an isomorphism is a transformation that maintains the similarity between two structures, making them equivalent in many aspects. This concept is important in abstract algebra and group theory, as it allows mathematicians to identify and compare different structures that have the same underlying properties.
Isomorphous
Isomorphous (adjective): Having the same crystal structure and similar chemical composition, but with different chemical properties. In other words, isomorphous substances are atoms or molecules that have the same arrangement of atoms in a crystal, but differ in their chemical makeup or atomic composition.
Isomorphy
Isoneph
Isonephelic
Isonephelic refers to having or denoting the same angle of incidence and refraction. In other words, it describes the phenomenon where a bundle of rays passes through a medium, such as a prism or a lens, without being refracted or bent, maintaining its original angle of incidence.
Isoniazid
Isonicotinamide
Isonicotine