How can we prove that the vector space of polynomials in one variable, $\mathbb{R}[x]$ is not finite dimensional?
[Math] Proof that $\mathbb{R}[x]$ is not a finite dimensional vector space
abstract-algebralinear algebrapolynomialsvector-spaces
abstract-algebralinear algebrapolynomialsvector-spaces
How can we prove that the vector space of polynomials in one variable, $\mathbb{R}[x]$ is not finite dimensional?
Best Answer
It has an infinite linearly independent set, $\{1,x,x^2,x^3,\dots\}$.