Is $S=\{(1,t)\mid t\in \mathbb{R}\}$ a subspace of $\mathbb{R}^2$? My professor introduced subspaces of $\mathbb{R}^n$ today and I don't think I understand them very well.
He posed this question as an example:

Is the set $S=\{(1,t)\mid t\in \mathbb{R}\}$ a subspace of $\mathbb{R}^2$?

He said that it wasn't. Could anyone elaborate as to why it isn't?
Can I simply say that the zero vector, $\vec{0}=(0,0)$ can never equal $(1,t)$ and be done with it?

YOU are right. Every vector space must have a zero. However set $S$ is not a vector subspace, though it is a topology subspace.
