It is isomorphic to $\mathbb{Z}_{2^8},$ only difference is the symbols usually identifying the elements of the set are from $\{-128, \ldots, 127 \}$ and not $\{0, \ldots, 256\}.$
What is an elegant way to say this in math?
It is isomorphic to $\mathbb{Z}_{2^8},$ only difference is the symbols usually identifying the elements of the set are from $\{-128, \ldots, 127 \}$ and not $\{0, \ldots, 256\}.$
What is an elegant way to say this in math?
A group needs to satisfy the group axioms, so you need to define the group operation. Presumably you are using addition modulo 256. There is a natural correspondence between the two sets that takes $n \in [-128,127]$ to $\begin {cases} n+256 & n \lt 0 \\n & n \ge 0 \end {cases}$ and you can show that the group structure is maintained.