Prove that all polynomials from $\mathbb{R}$ to $\mathbb{R}$ are continuous. Now this is from a topological point of view.
I thought that maybe induction would work here?
Initial Case: $f(x) = a_{0}$ where $a_{0} \in \mathbb{N}$. This is continuous.
Inductive Case: $f(x) = a_{0} + a_{1}x + a_{2}x^2 + ... + a_{n}x^n + ...$
Since the sum of continuous functions is continuous, this implies every term is continuous. Makes sense. Feel like theirs a lot of holes in my reasoning though. For one I am not sure how to show the constant $a_{0}$ is continuous from a topological view.