# 2016-20 Finding a subspace

Let $$V_1,V_2,\ldots$$ be countably many $$k$$-dimensional subspaces of $$\mathbb{R}^n$$. Prove that there exists an $$(n-k)$$-dimensional subspace $$W$$ of $$\mathbb{R}^n$$ such that $$\dim V_i\cap W=0$$ for all $$i$$.

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