(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let {W_1,W_2,W_3,...} be a collection of proper subspaces of V (i.e. W_i not=V) such that W_i is a subset of W_(i+1) for all i. Prove that U(W_i) (i from 1 to infinity) is a proper subspace of V

3. The attempt at a solution

I've already proven that U(W_i) is a subspace of V, so I only need to show that U(W_i) not= V. I've used induction but that only proves that W_i (i from 1 to n) is a proper subset of V, not U(W_i) (i from 1 to infinity). How do I show that U(W_i) (i from 1 to infinity) is a proper subset of V? I'm familiar with infinite set theory stuff (axiom of choice, etc...), but I don't know how to use it here. I could not use dimensions to help me because infinity minus a number is still infinity. Should I use the complement subsets of W_i?

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# Homework Help: Subspaces of a vector space

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