# Math Help - Which of the two is proper math notation?

1. ## Which of the two is proper math notation?

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!
2. I think that "u+v is in subspace S" is equivalent to "u+v is in S, which is a subspace". Then this is written as $u+v\in S$.
3. Emakarov is correct. In addition, I would say that the notation $u\in S$ means that $u$ is one object, and it is a member of the set $S.$ The second notation you mentioned is (I think) $U\subset S,$ and this means that $U$ is a set, and every element in $U$ is also in $S.$ So, $\in$ corresponds to one element being in a set, whereas $\subset$ corresponds to what's on the left being a subset of what's on the right. Make sense?