# What are some examples of infinite dimensional vector spaces?

I would like to have some examples of infinite dimensional vector spaces that help me to break my habit of thinking of $$\mathbb{R}^n$$ when thinking about vector spaces.

1. $\Bbb R[x]$, the polynomials in one variable.
2. All the continuous functions from $\Bbb R$ to itself.
3. All the differentiable functions from $\Bbb R$ to itself. Generally we can talk about other families of functions which are closed under addition and scalar multiplication.
4. All the infinite sequences over $\Bbb R$.