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HungryChemist
HungryChemist is offline
#13
Aug5-05, 02:20 AM
P: 144
Quote 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:
[latex]\emptyset=\{x\in{M}|x\neq{x}\}[/latex]

...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 [latex]\emptyset=\{x\in{M}|x\neq{y}\}[/latex]?

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