Thread: Empty Set and Vector Space View Single Post
P: 144
 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 non-empty set. If we have a property which no elements of a non-empty set have, we obtain the empty subset of this non-empty set: $\emptyset=\{x\in{M}|x\neq{x}\}$ ...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 $\emptyset=\{x\in{M}|x\neq{y}\}$?

x not equal x sounds very wrong.....