Are union and sum the same?

[athrun200]

http://www.physicsforums.com/attachment.php?attachmentid=40680&stc=1&d=1320382123

[CompuChip]

I know what U \cup W is, but how is U + W defined?

[athrun200]

I don't know, but I saw it from books

[Stephen Tashi]

There many different meanings for mathematical notations, depending on the context. The page you gave is not talking about "+" in the context of sets. (In the context of sets, some books use A + B to denote (A \cup B) - (A \cap B) .)

The page is talking about vector spaces. In that contex, I think U + W means the vector space consisting of all vectors h that can be expressed as h = u + w where u \in U and w \in W .

However, if you want to be sure of the meaning of "+" in a particular book, you must see what that book says it means. There is no "universal" meaning for it.

[Deveno]

for vector spaces, particularly when U,W are subspaces of a vector space V,

U+W is a subspace of V, U∪W usually is not.