Not necessarily; You see, in G-{0, 1}, there is a crooked thief with a complicated curve, which is the same as 0, but different from 0.

Isomorphism is a kind of mapping defined between mathematical objects, which can reveal the relationship between the attributes or operations of these objects. If there is isomorphic mapping between two mathematical structures, then the two structures are called isomorphic. Generally speaking, if the specific definitions of the properties or operations of homogeneous objects are ignored, homogeneous objects are completely equivalent only in terms of structure.

Common isomorphism includes: automorphism, group isomorphism, ring isomorphism, domain isomorphism and vector space isomorphism, in which automorphism is defined as: E and F have two groups, and there is an operation on E and F, which we call (sign replaceable) * and. It is closed for e, f, *, and respectively (that is, the elements in any two sets are still elements of the set after operation.

We say that F is isomorphic if and only if f ∈ γ (e, f) and F are bijective and f (a * b) = f (a) f (b) exists for any element in E. If the above E and F are the same set E, F is said to be automorphism.