[Tainnor]

I think you are confused about the analogies at the beginning at the article (although there is nothing technically wrong about them).

Here's the definition of a vector space which agrees with the one everyone in mathematics use: https://thenumb.at/Functions-are-Vectors/#vector-spaces

From this it's fairly easy to prove (and done in the article) that the set of all functions R->R is a vector space.

[ttoinou]

I understand that. The crux of the article is supposedly being able to apply what we learned with easy small vector space to infinite function vector space : we can't. But he's taking the example of polynomials and analytical functions which are MUCH smaller spaces than functions in general.

[Tainnor]

Yes we can. Several people have tried explaining this to you. Maybe you should sit down and work through the material.

[ttoinou]

Maybe you could envision that I learned maths a similar way than you and that's why I have problem with this material. It's trying to portray complicated space as simple, they're not