Isomorphism

An isomorphism is a structure-preserving Bijection between two mathematical objects.

• Notation: $A\cong B$ (read: ”$A$ is isomorphic to $B$”)

Meaning:

• They are not literally equal, but there exists a bijective correspondence between their elements (and possibly operations, depending on context).
• Example: The Cartesian Products $A\times B$ and $B\times A$ are isomorphic, since there is a natural bijection mapping $(a,b)\mapsto (b,a)$