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Definition Let $V$ be vector space over $K$. Let $U\subseteq V$ be a subset. Suppose that

  • for all $u_{1},u_{2}\in U$, $u_{1}+u_{2}\in U$
  • for all $u\in U$ and $\alpha\in K$, $\alpha u\in U$
  • $U$ is not empty.

My quiston is: I think, $1$ and $0$ should be in $U$ but there is not in the definition. Should there these in the definition?

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    Let alpha be 0 in the second item, no? – 2017-02-20
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    @The Chaz 2.0 for $\alpha=0$, this would work. I don't know what OP means with $1 \in U$, since $1$ is not a vector. – 2017-02-20
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    @SimonMarynissen $1$ is multiplicative inverse, isn't it? Then, why $1$ is not a vector? – 2017-02-20
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    $1$ is an element of $K$ not of $V$ – 2017-02-20

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