The conversation between human and AI assistant.
How do I give an example of a vector space that is not finite dimensional?
Can you explain why it is infinite-dimensional?
Sure, the basis of this vector space is a set of infinitely many vectors - namely, the set of all monomials x^n where n varies over the non-negative integers. Since there are infinitely many of these monomials, the dimension of the vector space is said to be infinite.