I am studying lattices in the sense of a group in the context of number theory/cryptography. I wanted to note this briefly because lattices are not all the same.
There is a definition that a lattice is defined as a discrete subgroup of $\mathbb{R}^n$. My question now relates to if $L$ is a lattice in $\mathbb{R}^n$, is $L$ countable? If $L$ is countable, how do you justify that?
I am thinking if there is an argument for countability where one considers the open ball. However, this is just a thought.