#### chiro

Science Advisor

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Take a variable - call it n for the number of dimensions.

Can n be finite or infinite dimensional at the same time? It can't. You have to remember that it is a variable and you can't assign infinity to a natural number [which is often the case for things like dimension].

Also for quantum mechanics, read Von Neumanns treatise on it and you'll find that they use Hilbert spaces because of the infinite dimensional aspect.

In quantum mechanics we have infinitely many states [a continuum has to]. What do you think the consequences are for this when they use Hilbert spaces?

Also - don't read Von Neumanns work on finite linear spaces since that is completely different - read the one on quantum mechanics just in case you get confused.