Isomorphism

Uncommon card · No. 102224

In mathematics, an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between them, and this is often denoted as ⁠ A ≅ B {\displaystyle A\cong B} ⁠. The word is derived from Ancient Greek ἴσος (isos) 'equal' and μορφή (morphe) 'form, shape'. The interest in isomorphisms lies in the fact that two isomorphic objects have the same properties, from the point of view of the structure considered (excluding further information such as additional structure or names of objects). Thus isomorphic structures may often be identified, that is, considered the same. One says also that the two structures are the same up to an isomorphism. For example, there are several different ways for defining the real numbers, and despite the different nature of the resulting objects (sequences of digits...

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