Quote by symplectic_manifold
Well, this is it.
The empty set is a subset of every set exactly because of the fact, that one doesn't need to verify, that every element of the empty set also belongs to a nonempty set.
If we have a property which no elements of a nonempty set have, we obtain the empty subset of this nonempty set:
[itex]\emptyset=\{x\in{M}x\neq{x}\}[/itex]
...but as I eventually made clear for myself, it has nothing to do with a vector space...nothing can be defined on an empty set...from nothing comes nothing!

shoudn't it be [itex]\emptyset=\{x\in{M}x\neq{y}\}[/itex]?
x not equal x sounds very wrong.....