isomorphic

See also: isomorphism

created by Actuary X

(idea) by Actuary X (6.2 y) (print) ? (I like it!) Sat Nov 13 1999 at 10:10:15

A one-to-one correspondence of a set A with a set B. The sets A and B are then said to be equinumerable, equipotent or equivalent.

If operations such as addition or multiplication are defined for A and B, it is required that these correspond between A and B.

(idea) by Pantsless Bob (3.4 mon) (print) ? (I like it!) Tue Apr 16 2002 at 23:09:35

Two groups are said to be isomorphic if there exists a map f: G₁->G₂ such that f is a bijection. Let G₁ be (G,+) and let G₂ be (H,*), where G and H are arbitrary non-empty sets and + and * are arbitrary operations on those sets. For g₁, g₂ in G, f(g₁ + g₂) = f(g₁) * f(g₂) => G₁ and G₂ are isomorphic.

(definition) by Webster 1913 (print) Wed Dec 22 1999 at 0:33:46

I`so*mor"phic (?), a.

Isomorphous.

I`so*mor"phic (?), a. (Biol.)

Alike in form; exhibiting isomorphism.

printable version
chaos

isomorphism	How your brain codes knowledge	All finite fields are isomorphic to GF(p^n)	bijection
Ook!	Cayley's Theorem	The M&M law of simplicity	Galois Field
field extension	ring homomorphism	On computable numbers, with an application to the Entscheidungsproblem	Graph isomorphism
How a computer works	Fundamental theorem of finite abelian groups	Banach space	dual of a vector space
Map	Abstraction and Cognitive Modalities	ambiguity	HOWTO: Build a lasting peace in the Middle East
Isomorphous	semidirect product	finitely presented group	Polynomial

Y'know, if you log in, you can write something here, or contact authors directly on the site. Create a New User if you don't already have an account.

Login
Password

remember me
password reminder
register

Everything2 Help

Look at this mess the Death Borg made!
Villages in Germany are three kilotons apart
The world breaks everyone
Antietam
Attention
torque
Dover test
Some people break so easily
Giving Your Cat a Pill (and your little dog, too!)
Quantum Quake
Egg Drop
Pithing the frog
Danse Macabre
Kit Kat Konspiracy

Alnilamski
Rebel Yell	(thing)
Heisenberg
Dahon Speed D7	(thing)
etgar
Protection of civil rights in the USA and UK	(essay)
archiewood
Airspace classifications	(idea)
Ouzo
My first Christmas	(event)
TheDeadGuy
Editor Log: August 2008	(log)
AspieDad
Tools of the Trade	(essay)
Apatrix
Editor Log: August 2008	(log)
etouffee
Back where we started	(poetry)
NeverLost
I'm never getting drunk again	(idea)
Noung
post-racial	(idea)
Heitah
Intensive farming	(essay)
XWiz
Big Science	(review)
Wuukiee
yellow cake batter	(recipe)
Pavlovna
Sassenach	(person)

Everything 2 is brought to you by the letter C and The Everything Development Company