If I want to say that "u+v is in subspace S" do I say "u + v element of S" or "u+v the sideways upside down U of S"?
Any input would be greatly appreciated!
Thanks in advance!
Emakarov is correct. In addition, I would say that the notation $\displaystyle u\in S$ means that $\displaystyle u$ is one object, and it is a member of the set $\displaystyle S.$ The second notation you mentioned is (I think) $\displaystyle U\subset S,$ and this means that $\displaystyle U$ is a set, and every element in $\displaystyle U$ is also in $\displaystyle S.$ So, $\displaystyle \in$ corresponds to one element being in a set, whereas $\displaystyle \subset$ corresponds to what's on the left being a subset of what's on the right. Make sense?