I 'm studying about Hilbert Spaces this semester, and the following is a Proposition from yesterday's class which I can't completely understand.
"Obviously,the closed linear span of $V\;$ coincides with $H$."
It doesn't seem so obvious to me. It might be really silly, but how do I know that the closed linear span of a dense subset of $H$ is also dense in $H$? I have the feeling that it's quite elementary but I'm new to Functional Analysis.
I would appreciate any help. Thanks in advnace!!