【归档】给出R^2的一个非空子集U的例子，使得U对于加法是封闭并且具有加法逆元的，但U不是R^2的子空间

Note: 旧的wordpress博客弃用，于是将以前的笔记搬运回来。

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Question:
Give a example of a nonempty subset $U$ of ${\mathbb{R}}^2$ such that $U$ is closed under addition and under taking additive inverses but U is not a subspace of ${\mathbb{R}}^2$.
Solution:
Consider the subset ${\mathbb{Z}}^2$. This set is closed under addition, as we will g