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## Homework Statement

Prove that the intersection of any collection of subspaces of V is a subspace of V.

Okay, so I had to look up on wiki what an intersection is. To my understanding, it is basically the 'place' where sets or spaces 'overlap.'

I am not sure how to construct the problem in the language of math.

If U

_{1},...,U

_{n}are subspaces of

*V*then I have show that their intersection includes the additive ID and is closed under addition and scalar multiplication.

can someone give me a kick in the right direction?