Isomorphism
An isomorphism is a matching between two structures that pairs their members one to one and preserves every operation, so that anything true of one structure in its own terms is true of the other. Two isomorphic structures may be built from completely different material and still be the same object as far as mathematics is concerned. The word means equal shape, and the point is that mathematics identifies things by how they behave rather than by what they are made of.
Why it matters
It explains why a theorem proved once can be reused in an unrelated field, and it is the reason abstraction pays for itself.
Also written: isomorphic, isomorphisms
Where it comes up
Read about Isomorphism on Wikipedia
Sources
- Isomorphism Wikipedia
- Group (mathematics) WikipediaGroups are where isomorphism is easiest to see in action.
