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So this is about vector spaces. I know these are sort of abstract spaces but I'd like more explanation on them.

1) [tex] \mathbb{R} [/tex] This is the space of real vectors right, like from real numbers?

2) [tex] \mathbb{P} [/tex] What does this mean that it's a polynomial space? Like the standard basis is {1,t,t

^{2},t

^{3}...} but how is [tex] \mathbb{P}_n[/tex] different from [tex] \mathbb{R}^n [/tex]

3) [tex] \mathbb{C} [/tex] My instructor basically showed us this one, but didn't explain it cause we don't use it in our linear algebra class.

Edit: Are there any other majors spaces that I didn't list but are important to know?