Prove that any subspace, W, of a finite-dimensional vector space V must also be finite dimensional.
Prove subspace of finite dimensional vector space is finite dimensional
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$\begingroup$
linear-algebra
proof-writing
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2Suppose for sake of contradiction that *W* isn't finite dimensional. That will probably contradict *V* being finite dimensional. – 2012-11-18
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1I'd rather not without first seeing what you've done. Mind showing us your work and where you got stuck? – 2012-11-18
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0@Neal Well my professor gave a hint saying we can use the Plus-minus theorem to prove this but i'm not sure how to go about proving this using plus-minus theorem. – 2012-11-18
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0You don't have to use the plus-minus theorem, but if you really want to, try to think of a set of vectors to apply the "plus" or the "minus" to yield a contradiction with *W* being finite dimensional. – 2012-11-19