bymathbbZ2
The notation $ \mathbb{Z}_2 $ or $ \mathbb{Z}/2\mathbb{Z} $ refers to the set of integers modulo 2. This set consists of only two elements, typically represented as 0 and 1. Arithmetic in $ \mathbb{Z}_2 $ is performed using modular arithmetic with a modulus of 2. This means that any integer when divided by 2 will have a remainder of either 0 or 1.
The addition operation in $ \mathbb{Z}_2 $ is defined as follows:
1 + 1 = 0 (since 2 divided by 2 has a remainder of 0)
The multiplication operation in $ \mathbb{Z}_2 $ is defined as follows:
The set $ \mathbb{Z}_2 $ with these operations forms a field, which is a fundamental algebraic structure in
In computer science, $ \mathbb{Z}_2 $ is particularly important as it corresponds directly to binary values (0 and