When talking about vector space, you usually need the “scalar (field)”, and scalars need inverse to be well-defined.
So for integers, the scalar should be integer itself.
Sadly, inverse of integers stops being an integer, from where all sorts of number theoretic nightmare occurs
Instead, integers form a ring, and is a module over scalar of integers.
wow didn’t expect this to be so general. How do integers not fit into the definition ? you can add them together and obtain another integer
When talking about vector space, you usually need the “scalar (field)”, and scalars need inverse to be well-defined.
So for integers, the scalar should be integer itself. Sadly, inverse of integers stops being an integer,
from where all sorts of number theoretic nightmare occursInstead, integers form a ring, and is a module over scalar of integers.