Z/Modulo/Equivalence relation/Example

Let ${}d\in \mathbb {N}$ be fixed. We consider on ${}\mathbb {Z}$ the equivalence relation ${}\sim$, where two numbers ${}a,b\in \mathbb {Z}$ are considered to be equivalent if their difference ${}a-b$ is a multiple of ${}d$. Two numbers are equivalent if and only if it is possible to reach from one number the other number by jumps of length ${}d$. Using division with remainder, this means that two numbers are equivalent to each other if, upon division by ${}d$, they leave the same remainder.