Isomorphism is a very general concept that appears in several areas of mathematics. The word derives from the Greek iso, meaning "equal," and morphosis, meaning "to form" or "to shape."
Formally, an isomorphism is bijective morphism. Informally, an isomorphism is a map that preserves sets and relations among elements.
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is isomorphic to 
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is written 
.
Unfortunately, this symbol is also used to denote geometric congruence.
An isomorphism from a set of elements onto itself is called an automorphism.
