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 that is also an infinite-dimensional space?
Sure. Similar to the previous example, the basis of this vector space is a set of infinitely many vectors - namely, the set of all sequences having a 1 in one position and zeros elsewhere. Since there are infinitely many such sequences, the dimension of the vector space is said to be infinite.