Strictly speaking, two structures are defined as isomorphic if their elements correspond to each other and satisfy the same operation. For example, 1 corresponding to 1, 2 corresponding to 2, 1+ 1=2 corresponding to the past and then written as one plus one equals two, which is exactly the same as the original definition of addition.
The deeper concept is partial isomorphism, in other words, only when only one operation is considered, the two are consistent. Semi-integers (0, 1/2, 1, 3/2, 2, 5/2, …,-1/2, -3/2, -2, …) and integers are an example. We can regard 1 in an integer as 1/2 in a semi-integer, and n in an integer corresponds to n/2 in a semi-integer. If only addition is considered, two Abelian groups are isomorphic! It can be understood that 1 in an integer is regarded as an addition unit, and 2 is regarded as two units, so 1/2 becomes a semi-integer unit. However, you may ask, (1/2)×(3/2)=3/4? This actually shows that semi-integers can only be groups, but not rings. It has only one addition structure, which is the same as the addition structure of integers. More generally, {0/n, 1/n, 2/n, …,- 1/n, -2/n} also has the same addition structure as integers. There is nothing special.
In the last article, the semi-integer of 1 can be regarded as both a literal and an integer of 1, and its connotation can be regarded as an integer of 2. This same and different nature, isomorphic and different structure, identity and difference contain profound philosophical thoughts. It has always been the core task of algebra to study whether algebraic structures are isomorphic and how many algebraic structures are different from each other.