[ttoinou]

I learned vector spaces in maths and I'm aware of your definition, that's how I learned it. I'm also aware that the same word can be used with different meanings depending on the context.

  (Imagine/remember what it feels like when children first learn that the integers aren't the only number, there are also fractions, then irrationals, then complex numbers...this is a very similar situation).

Imagine now an article saying "complex numbers are just natural numbers, you can apply euclidean division to them the exact same way"