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mathmari

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MHB

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Hey!

Let $1\leq n\in \mathbb{N}$ and let $U_1, U_2$ be subspaces of the $\mathbb{R}$-vector space $\mathbb{R}^n$.

I want to prove or disprove the following:

Let $1\leq n\in \mathbb{N}$ and let $U_1, U_2$ be subspaces of the $\mathbb{R}$-vector space $\mathbb{R}^n$.

I want to prove or disprove the following:

- The set $\{f\in \mathbb{R}^{\mathbb{R}} \mid \exists x\in \mathbb{R} : f(x)=0_{\mathbb{R}}\}$ is a subspace of $\mathbb{R}^{\mathbb{R}}$.

What exactly is $\mathbb{R}^{\mathbb{R}}$ ?

$ $

- The set $U_1+U_2$ is a subspace of $\mathbb{Q}^n$.

I have shown that $U_1+U_2$ is a subspace of $\mathbb{R}^n$. I think that the sum $U_1+U_2$ doesn't have to be also a subspace of $\mathbb{Q}^n$. Is this correct?

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