technically that holds true for all real number representations of vectors we have. your computer computes stuff in "pretend" vector spaces and it just happens to approximately work out. Sometimes you have to care about the numerics, but most of the time you are fine.

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//edit Having said that, there are ways to make it mathematically work. A vector space is typically defined over a field, e.g., the real or complex numbers, and in this case the scalars are limited to that field. The same construction over a ring (like the integers) is called a module. So a quantized vector (for example the integers) limited to scalars being integers as well DOES work out. The only thing you have to deal with is that divison in a ring might not exist.