In Linear Algebra we often talk about vector spaces and the defined operations there ( excuse my english, I hope I can get my point across ). But whenever infinite sums come up or the possibility thereof, the professor strictly prohibits them and always mentions that they must be finite.
I currently read additional literature and everywhere you find "remember, XYZ must be finite!".
Wikipedia ( in an article about the basis vector ) says: "The sums in the above definition are all finite because without additional structure the axioms of a vector space do not permit us to meaningfully speak about an infinite sum of vectors."
Still, this doesn't make it very clear to me, what the problem is. In calculus you can talk about them just fine and they have lots of nice properties, too.
What is it about Linear Algebra, that makes infinite sums meaningless?